Q1. Find the midpoint of the line segment joining \((4, 5)\) and \((-8, 2)\).

A) -4, 7
B) -2.0, 1.5
C) 6.0, 1.5
D) -2.0, 3.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{4+-8}{2}, \frac{5+2}{2}\right)\)

\(= (-2.0, 3.5)\)

Q2. Find the midpoint of the line segment joining \((-3, -5)\) and \((-8, 1)\).

A) -5.5, -3.0
B) -11, -4
C) -5.5, -2.0
D) 2.5, -3.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-3+-8}{2}, \frac{-5+1}{2}\right)\)

\(= (-5.5, -2.0)\)

Q3. Find the midpoint of the line segment joining \((-10, -2)\) and \((-10, -1)\).

A) -10.0, -0.5
B) -20, -3
C) 0.0, -0.5
D) -10.0, -1.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-10+-10}{2}, \frac{-2+-1}{2}\right)\)

\(= (-10.0, -1.5)\)

Q4. Find the midpoint of the line segment joining \((3, -3)\) and \((10, -5)\).

A) -3.5, 1.0
B) 13, -8
C) 6.5, -4.0
D) 6.5, 1.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{3+10}{2}, \frac{-3+-5}{2}\right)\)

\(= (6.5, -4.0)\)

Q5. Find the midpoint of the line segment joining \((-5, -3)\) and \((8, -1)\).

A) -6.5, -1.0
B) 1.5, -1.0
C) 1.5, -2.0
D) 3, -4

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-5+8}{2}, \frac{-3+-1}{2}\right)\)

\(= (1.5, -2.0)\)

Q6. Find the midpoint of the line segment joining \((7, -2)\) and \((-2, -5)\).

A) 5, -7
B) 2.5, 1.5
C) 2.5, -3.5
D) 4.5, 1.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{7+-2}{2}, \frac{-2+-5}{2}\right)\)

\(= (2.5, -3.5)\)

Q7. Find the midpoint of the line segment joining \((-5, -3)\) and \((1, -10)\).

A) -4, -13
B) -3.0, 3.5
C) -2.0, -6.5
D) -2.0, 3.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-5+1}{2}, \frac{-3+-10}{2}\right)\)

\(= (-2.0, -6.5)\)

Q8. Find the midpoint of the line segment joining \((5, -1)\) and \((4, 6)\).

A) 0.5, -3.5
B) 9, 5
C) 4.5, 2.5
D) 4.5, -3.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{5+4}{2}, \frac{-1+6}{2}\right)\)

\(= (4.5, 2.5)\)

Q9. Find the midpoint of the line segment joining \((-10, -10)\) and \((1, -7)\).

A) -4.5, -8.5
B) -4.5, -1.5
C) -5.5, -1.5
D) -9, -17

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-10+1}{2}, \frac{-10+-7}{2}\right)\)

\(= (-4.5, -8.5)\)

Q10. Find the midpoint of the line segment joining \((9, -6)\) and \((0, 7)\).

A) N/A (1)
B) 4.5, -6.5
C) 9, 1
D) 4.5, 0.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{9+0}{2}, \frac{-6+7}{2}\right)\)

\(= (4.5, 0.5)\)

Q11. Find the midpoint of the line segment joining \((-1, -10)\) and \((7, 0)\).

A) 6, -10
B) -4.0, -5.0
C) 3.0, -5.0
D) N/A (1)

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-1+7}{2}, \frac{-10+0}{2}\right)\)

\(= (3.0, -5.0)\)

Q12. Find the midpoint of the line segment joining \((3, -9)\) and \((3, 9)\).

A) 6, 0
B) 3.0, -9.0
C) 3.0, 0.0
D) 0.0, -9.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{3+3}{2}, \frac{-9+9}{2}\right)\)

\(= (3.0, 0.0)\)

Q13. Find the midpoint of the line segment joining \((0, -3)\) and \((10, 1)\).

A) 5.0, -2.0
B) 5.0, -1.0
C) -5.0, -2.0
D) 10, -2

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{0+10}{2}, \frac{-3+1}{2}\right)\)

\(= (5.0, -1.0)\)

Q14. Find the midpoint of the line segment joining \((-6, 5)\) and \((2, 9)\).

A) -2.0, -2.0
B) -4.0, -2.0
C) -4, 14
D) -2.0, 7.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-6+2}{2}, \frac{5+9}{2}\right)\)

\(= (-2.0, 7.0)\)

Q15. Find the midpoint of the line segment joining \((0, 5)\) and \((-7, -6)\).

A) 3.5, 5.5
B) -3.5, -0.5
C) -3.5, 5.5
D) -7, -1

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{0+-7}{2}, \frac{5+-6}{2}\right)\)

\(= (-3.5, -0.5)\)

Q16. Find the midpoint of the line segment joining \((-10, -7)\) and \((-8, -3)\).

A) -9.0, -2.0
B) -18, -10
C) -9.0, -5.0
D) -1.0, -2.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-10+-8}{2}, \frac{-7+-3}{2}\right)\)

\(= (-9.0, -5.0)\)

Q17. Find the midpoint of the line segment joining \((6, -9)\) and \((-7, 7)\).

A) -0.5, -8.0
B) -1, -2
C) 6.5, -8.0
D) -0.5, -1.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{6+-7}{2}, \frac{-9+7}{2}\right)\)

\(= (-0.5, -1.0)\)

Q18. Find the midpoint of the line segment joining \((-4, 2)\) and \((-1, 2)\).

A) -1.5, 0.0
B) -5, 4
C) -2.5, 2.0
D) -2.5, 0.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-4+-1}{2}, \frac{2+2}{2}\right)\)

\(= (-2.5, 2.0)\)

Q19. Find the midpoint of the line segment joining \((-5, -5)\) and \((-10, -1)\).

A) -15, -6
B) -7.5, -2.0
C) -7.5, -3.0
D) 2.5, -2.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-5+-10}{2}, \frac{-5+-1}{2}\right)\)

\(= (-7.5, -3.0)\)

Q20. Find the midpoint of the line segment joining \((3, -3)\) and \((-3, 4)\).

A) 0.0, -3.5
B) 3.0, -3.5
C) 0, 1
D) 0.0, 0.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{3+-3}{2}, \frac{-3+4}{2}\right)\)

\(= (0.0, 0.5)\)

Q21. Find the midpoint of the line segment joining \((1, 3)\) and \((9, 1)\).

A) -4.0, 1.0
B) 10, 4
C) 5.0, 2.0
D) 5.0, 1.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{1+9}{2}, \frac{3+1}{2}\right)\)

\(= (5.0, 2.0)\)

Q22. Find the midpoint of the line segment joining \((-6, 5)\) and \((6, 10)\).

A) 0.0, -2.5
B) 0, 15
C) -6.0, -2.5
D) 0.0, 7.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-6+6}{2}, \frac{5+10}{2}\right)\)

\(= (0.0, 7.5)\)

Q23. Find the midpoint of the line segment joining \((-4, 8)\) and \((7, -1)\).

A) 1.5, 4.5
B) 3, 7
C) 1.5, 3.5
D) -5.5, 4.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-4+7}{2}, \frac{8+-1}{2}\right)\)

\(= (1.5, 3.5)\)

Q24. Find the midpoint of the line segment joining \((-7, 2)\) and \((8, 0)\).

A) 0.5, 1.0
B) 1, 2
C) -7.5, 1.0
D) N/A (1)

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-7+8}{2}, \frac{2+0}{2}\right)\)

\(= (0.5, 1.0)\)

Q25. Find the midpoint of the line segment joining \((-2, -4)\) and \((4, 6)\).

A) -3.0, -5.0
B) 1.0, 1.0
C) 2, 2
D) 1.0, -5.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-2+4}{2}, \frac{-4+6}{2}\right)\)

\(= (1.0, 1.0)\)

Q26. Find the midpoint of the line segment joining \((8, -1)\) and \((9, 3)\).

A) 8.5, 1.0
B) -0.5, -2.0
C) 17, 2
D) 8.5, -2.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{8+9}{2}, \frac{-1+3}{2}\right)\)

\(= (8.5, 1.0)\)

Q27. Find the midpoint of the line segment joining \((-8, 2)\) and \((9, 0)\).

A) 0.5, 1.0
B) 1, 2
C) N/A (1)
D) -8.5, 1.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-8+9}{2}, \frac{2+0}{2}\right)\)

\(= (0.5, 1.0)\)

Q28. Find the midpoint of the line segment joining \((1, -7)\) and \((6, -5)\).

A) 7, -12
B) 3.5, -6.0
C) 3.5, -1.0
D) -2.5, -1.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{1+6}{2}, \frac{-7+-5}{2}\right)\)

\(= (3.5, -6.0)\)

Q29. Find the midpoint of the line segment joining \((-10, -7)\) and \((-7, -3)\).

A) -8.5, -2.0
B) -17, -10
C) -8.5, -5.0
D) -1.5, -2.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-10+-7}{2}, \frac{-7+-3}{2}\right)\)

\(= (-8.5, -5.0)\)

Q30. Find the midpoint of the line segment joining \((6, -4)\) and \((-8, 7)\).

A) 7.0, -5.5
B) -1.0, -5.5
C) -1.0, 1.5
D) -2, 3

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{6+-8}{2}, \frac{-4+7}{2}\right)\)

\(= (-1.0, 1.5)\)

Q31. Find the midpoint of the line segment joining \((-6, 10)\) and \((-6, 2)\).

A) -6.0, 4.0
B) -12, 12
C) 0.0, 4.0
D) -6.0, 6.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-6+-6}{2}, \frac{10+2}{2}\right)\)

\(= (-6.0, 6.0)\)

Q32. Find the midpoint of the line segment joining \((-6, -5)\) and \((3, 2)\).

A) -4.5, -3.5
B) -1.5, -3.5
C) -1.5, -1.5
D) -3, -3

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-6+3}{2}, \frac{-5+2}{2}\right)\)

\(= (-1.5, -1.5)\)

Q33. Find the midpoint of the line segment joining \((3, 7)\) and \((-2, 5)\).

A) 0.5, 1.0
B) 0.5, 6.0
C) 1, 12
D) 2.5, 1.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{3+-2}{2}, \frac{7+5}{2}\right)\)

\(= (0.5, 6.0)\)

Q34. Find the midpoint of the line segment joining \((3, -6)\) and \((10, -3)\).

A) 6.5, -1.5
B) 13, -9
C) 6.5, -4.5
D) -3.5, -1.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{3+10}{2}, \frac{-6+-3}{2}\right)\)

\(= (6.5, -4.5)\)

Q35. Find the midpoint of the line segment joining \((7, 4)\) and \((2, -1)\).

A) 9, 3
B) 2.5, 2.5
C) 4.5, 1.5
D) 4.5, 2.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{7+2}{2}, \frac{4+-1}{2}\right)\)

\(= (4.5, 1.5)\)

Q36. Find the midpoint of the line segment joining \((-7, -3)\) and \((3, 4)\).

A) -4, 1
B) -2.0, 0.5
C) -5.0, -3.5
D) -2.0, -3.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-7+3}{2}, \frac{-3+4}{2}\right)\)

\(= (-2.0, 0.5)\)

Q37. Find the midpoint of the line segment joining \((-3, -3)\) and \((-2, -2)\).

A) -0.5, -0.5
B) -2.5, -0.5
C) -5, -5
D) -2.5, -2.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-3+-2}{2}, \frac{-3+-2}{2}\right)\)

\(= (-2.5, -2.5)\)

Q38. Find the midpoint of the line segment joining \((-10, -3)\) and \((4, -5)\).

A) -3.0, -4.0
B) -7.0, 1.0
C) -6, -8
D) -3.0, 1.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-10+4}{2}, \frac{-3+-5}{2}\right)\)

\(= (-3.0, -4.0)\)

Q39. Find the midpoint of the line segment joining \((-10, 4)\) and \((-10, 6)\).

A) -20, 10
B) -10.0, 5.0
C) -10.0, -1.0
D) 0.0, -1.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-10+-10}{2}, \frac{4+6}{2}\right)\)

\(= (-10.0, 5.0)\)

Q40. Find the midpoint of the line segment joining \((0, 6)\) and \((8, 5)\).

A) 4.0, 5.5
B) 8, 11
C) 4.0, 0.5
D) -4.0, 0.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{0+8}{2}, \frac{6+5}{2}\right)\)

\(= (4.0, 5.5)\)

Q41. Find the midpoint of the line segment joining \((1, -10)\) and \((-1, 2)\).

A) 1.0, -6.0
B) 0.0, -6.0
C) 0, -8
D) 0.0, -4.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{1+-1}{2}, \frac{-10+2}{2}\right)\)

\(= (0.0, -4.0)\)

Q42. Find the midpoint of the line segment joining \((-9, 0)\) and \((-1, 9)\).

A) -5.0, 4.5
B) -10, 9
C) -5.0, -4.5
D) -4.0, -4.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-9+-1}{2}, \frac{0+9}{2}\right)\)

\(= (-5.0, 4.5)\)

Q43. Find the midpoint of the line segment joining \((-6, -1)\) and \((-5, 2)\).

A) -0.5, -1.5
B) -11, 1
C) -5.5, 0.5
D) -5.5, -1.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-6+-5}{2}, \frac{-1+2}{2}\right)\)

\(= (-5.5, 0.5)\)

Q44. Find the midpoint of the line segment joining \((9, -10)\) and \((-9, 7)\).

A) 0.0, -8.5
B) 0, -3
C) 0.0, -1.5
D) 9.0, -8.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{9+-9}{2}, \frac{-10+7}{2}\right)\)

\(= (0.0, -1.5)\)

Q45. Find the midpoint of the line segment joining \((7, -8)\) and \((-4, 0)\).

A) 5.5, -4.0
B) 3, -8
C) N/A (1)
D) 1.5, -4.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{7+-4}{2}, \frac{-8+0}{2}\right)\)

\(= (1.5, -4.0)\)

Q46. Find the midpoint of the line segment joining \((-6, -9)\) and \((-3, -4)\).

A) -1.5, -2.5
B) -9, -13
C) -4.5, -2.5
D) -4.5, -6.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-6+-3}{2}, \frac{-9+-4}{2}\right)\)

\(= (-4.5, -6.5)\)

Q47. Find the midpoint of the line segment joining \((1, 10)\) and \((5, 8)\).

A) 6, 18
B) 3.0, 9.0
C) 3.0, 1.0
D) -2.0, 1.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{1+5}{2}, \frac{10+8}{2}\right)\)

\(= (3.0, 9.0)\)

Q48. Find the midpoint of the line segment joining \((3, 5)\) and \((4, 10)\).

A) 3.5, -2.5
B) -0.5, -2.5
C) 7, 15
D) 3.5, 7.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{3+4}{2}, \frac{5+10}{2}\right)\)

\(= (3.5, 7.5)\)

Q49. Find the midpoint of the line segment joining \((0, -9)\) and \((-3, 5)\).

A) -1.5, -2.0
B) -1.5, -7.0
C) 1.5, -7.0
D) -3, -4

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{0+-3}{2}, \frac{-9+5}{2}\right)\)

\(= (-1.5, -2.0)\)

Q50. Find the midpoint of the line segment joining \((-6, 10)\) and \((-8, 4)\).

A) -7.0, 3.0
B) -7.0, 7.0
C) 1.0, 3.0
D) -14, 14

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-6+-8}{2}, \frac{10+4}{2}\right)\)

\(= (-7.0, 7.0)\)

Q51. Find the midpoint of the line segment joining \((-9, -1)\) and \((-4, 2)\).

A) -6.5, -1.5
B) -2.5, -1.5
C) -6.5, 0.5
D) -13, 1

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-9+-4}{2}, \frac{-1+2}{2}\right)\)

\(= (-6.5, 0.5)\)

Q52. Find the midpoint of the line segment joining \((-5, -9)\) and \((-7, -9)\).

A) -6.0, -9.0
B) 1.0, 0.0
C) -6.0, 0.0
D) -12, -18

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-5+-7}{2}, \frac{-9+-9}{2}\right)\)

\(= (-6.0, -9.0)\)

Q53. Find the midpoint of the line segment joining \((5, -10)\) and \((-9, -4)\).

A) -2.0, -3.0
B) -4, -14
C) -2.0, -7.0
D) 7.0, -3.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{5+-9}{2}, \frac{-10+-4}{2}\right)\)

\(= (-2.0, -7.0)\)

Q54. Find the midpoint of the line segment joining \((-5, -10)\) and \((10, -2)\).

A) 2.5, -6.0
B) 2.5, -4.0
C) 5, -12
D) -7.5, -4.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-5+10}{2}, \frac{-10+-2}{2}\right)\)

\(= (2.5, -6.0)\)

Q55. Find the midpoint of the line segment joining \((1, -6)\) and \((-9, 1)\).

A) -4.0, -3.5
B) 5.0, -3.5
C) -4.0, -2.5
D) -8, -5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{1+-9}{2}, \frac{-6+1}{2}\right)\)

\(= (-4.0, -2.5)\)

Q56. Find the midpoint of the line segment joining \((0, -1)\) and \((4, 9)\).

A) 2.0, 4.0
B) 4, 8
C) -2.0, -5.0
D) 2.0, -5.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{0+4}{2}, \frac{-1+9}{2}\right)\)

\(= (2.0, 4.0)\)

Q57. Find the midpoint of the line segment joining \((6, 0)\) and \((1, 2)\).

A) 3.5, 1.0
B) 3.5, -1.0
C) 2.5, -1.0
D) 7, 2

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{6+1}{2}, \frac{0+2}{2}\right)\)

\(= (3.5, 1.0)\)

Q58. Find the midpoint of the line segment joining \((-8, -7)\) and \((2, -10)\).

A) -3.0, -8.5
B) -6, -17
C) -3.0, 1.5
D) -5.0, 1.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-8+2}{2}, \frac{-7+-10}{2}\right)\)

\(= (-3.0, -8.5)\)

Q59. Find the midpoint of the line segment joining \((-9, 6)\) and \((-7, 7)\).

A) -8.0, -0.5
B) -8.0, 6.5
C) -1.0, -0.5
D) -16, 13

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-9+-7}{2}, \frac{6+7}{2}\right)\)

\(= (-8.0, 6.5)\)

Q60. Find the midpoint of the line segment joining \((-6, 9)\) and \((-6, -4)\).

A) 0.0, 6.5
B) -6.0, 2.5
C) -6.0, 6.5
D) -12, 5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-6+-6}{2}, \frac{9+-4}{2}\right)\)

\(= (-6.0, 2.5)\)

Q61. Find the midpoint of the line segment joining \((7, -8)\) and \((-5, 4)\).

A) 1.0, -2.0
B) 6.0, -6.0
C) 2, -4
D) 1.0, -6.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{7+-5}{2}, \frac{-8+4}{2}\right)\)

\(= (1.0, -2.0)\)

Q62. Find the midpoint of the line segment joining \((-1, 4)\) and \((-4, -10)\).

A) -2.5, 7.0
B) 1.5, 7.0
C) -2.5, -3.0
D) -5, -6

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-1+-4}{2}, \frac{4+-10}{2}\right)\)

\(= (-2.5, -3.0)\)

Q63. Find the midpoint of the line segment joining \((3, 9)\) and \((-4, 3)\).

A) -0.5, 6.0
B) -1, 12
C) 3.5, 3.0
D) -0.5, 3.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{3+-4}{2}, \frac{9+3}{2}\right)\)

\(= (-0.5, 6.0)\)

Q64. Find the midpoint of the line segment joining \((6, -8)\) and \((-10, -5)\).

A) -2.0, -6.5
B) -4, -13
C) -2.0, -1.5
D) 8.0, -1.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{6+-10}{2}, \frac{-8+-5}{2}\right)\)

\(= (-2.0, -6.5)\)

Q65. Find the midpoint of the line segment joining \((-1, -2)\) and \((8, 2)\).

A) 7, 0
B) -4.5, -2.0
C) 3.5, 0.0
D) 3.5, -2.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-1+8}{2}, \frac{-2+2}{2}\right)\)

\(= (3.5, 0.0)\)

Q66. Find the midpoint of the line segment joining \((-10, -4)\) and \((-8, 10)\).

A) -1.0, -7.0
B) -9.0, 3.0
C) -9.0, -7.0
D) -18, 6

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-10+-8}{2}, \frac{-4+10}{2}\right)\)

\(= (-9.0, 3.0)\)

Q67. Find the midpoint of the line segment joining \((-6, -7)\) and \((0, 9)\).

A) -3.0, 1.0
B) N/A (1)
C) -3.0, -8.0
D) -6, 2

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-6+0}{2}, \frac{-7+9}{2}\right)\)

\(= (-3.0, 1.0)\)

Q68. Find the midpoint of the line segment joining \((-4, -2)\) and \((-1, -5)\).

A) -5, -7
B) -2.5, 1.5
C) -2.5, -3.5
D) -1.5, 1.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-4+-1}{2}, \frac{-2+-5}{2}\right)\)

\(= (-2.5, -3.5)\)

Q69. Find the midpoint of the line segment joining \((-2, 4)\) and \((1, -8)\).

A) -0.5, -2.0
B) -0.5, 6.0
C) -1, -4
D) -1.5, 6.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-2+1}{2}, \frac{4+-8}{2}\right)\)

\(= (-0.5, -2.0)\)

Q70. Find the midpoint of the line segment joining \((4, 3)\) and \((5, -3)\).

A) 4.5, 0.0
B) 4.5, 3.0
C) -0.5, 3.0
D) 9, 0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{4+5}{2}, \frac{3+-3}{2}\right)\)

\(= (4.5, 0.0)\)

Q71. Find the midpoint of the line segment joining \((-1, -5)\) and \((9, -10)\).

A) -5.0, 2.5
B) 8, -15
C) 4.0, 2.5
D) 4.0, -7.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-1+9}{2}, \frac{-5+-10}{2}\right)\)

\(= (4.0, -7.5)\)

Q72. Find the midpoint of the line segment joining \((-6, -1)\) and \((-6, -7)\).

A) 0.0, 3.0
B) -6.0, -4.0
C) -12, -8
D) -6.0, 3.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-6+-6}{2}, \frac{-1+-7}{2}\right)\)

\(= (-6.0, -4.0)\)

Q73. Find the midpoint of the line segment joining \((-10, 6)\) and \((-4, -5)\).

A) -7.0, 5.5
B) -3.0, 5.5
C) -7.0, 0.5
D) -14, 1

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-10+-4}{2}, \frac{6+-5}{2}\right)\)

\(= (-7.0, 0.5)\)

Q74. Find the midpoint of the line segment joining \((-10, 9)\) and \((10, 0)\).

A) 0.0, 4.5
B) 0, 9
C) N/A (1)
D) -10.0, 4.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-10+10}{2}, \frac{9+0}{2}\right)\)

\(= (0.0, 4.5)\)

Q75. Find the midpoint of the line segment joining \((8, -7)\) and \((-3, -5)\).

A) 5.5, -1.0
B) 5, -12
C) 2.5, -1.0
D) 2.5, -6.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{8+-3}{2}, \frac{-7+-5}{2}\right)\)

\(= (2.5, -6.0)\)

Q76. Find the midpoint of the line segment joining \((3, 2)\) and \((-5, 10)\).

A) 4.0, -4.0
B) -2, 12
C) -1.0, -4.0
D) -1.0, 6.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{3+-5}{2}, \frac{2+10}{2}\right)\)

\(= (-1.0, 6.0)\)

Q77. Find the midpoint of the line segment joining \((7, -3)\) and \((-2, -8)\).

A) 4.5, 2.5
B) 5, -11
C) 2.5, 2.5
D) 2.5, -5.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{7+-2}{2}, \frac{-3+-8}{2}\right)\)

\(= (2.5, -5.5)\)

Q78. Find the midpoint of the line segment joining \((10, 5)\) and \((8, -9)\).

A) 18, -4
B) 9.0, -2.0
C) 9.0, 7.0
D) 1.0, 7.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{10+8}{2}, \frac{5+-9}{2}\right)\)

\(= (9.0, -2.0)\)

Q79. Find the midpoint of the line segment joining \((7, 10)\) and \((-10, 0)\).

A) -1.5, 5.0
B) N/A (1)
C) 8.5, 5.0
D) -3, 10

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{7+-10}{2}, \frac{10+0}{2}\right)\)

\(= (-1.5, 5.0)\)

Q80. Find the midpoint of the line segment joining \((9, 3)\) and \((-7, -7)\).

A) 2, -4
B) 8.0, 5.0
C) 1.0, 5.0
D) 1.0, -2.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{9+-7}{2}, \frac{3+-7}{2}\right)\)

\(= (1.0, -2.0)\)

Q81. Find the midpoint of the line segment joining \((-1, -4)\) and \((-6, -9)\).

A) -3.5, -6.5
B) -7, -13
C) 2.5, 2.5
D) -3.5, 2.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-1+-6}{2}, \frac{-4+-9}{2}\right)\)

\(= (-3.5, -6.5)\)

Q82. Find the midpoint of the line segment joining \((5, 2)\) and \((8, 8)\).

A) -1.5, -3.0
B) 13, 10
C) 6.5, 5.0
D) 6.5, -3.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{5+8}{2}, \frac{2+8}{2}\right)\)

\(= (6.5, 5.0)\)

Q83. Find the midpoint of the line segment joining \((-8, 4)\) and \((-6, -4)\).

A) -14, 0
B) -7.0, 0.0
C) -1.0, 4.0
D) -7.0, 4.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-8+-6}{2}, \frac{4+-4}{2}\right)\)

\(= (-7.0, 0.0)\)

Q84. Find the midpoint of the line segment joining \((4, -4)\) and \((-8, 10)\).

A) -4, 6
B) 6.0, -7.0
C) -2.0, -7.0
D) -2.0, 3.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{4+-8}{2}, \frac{-4+10}{2}\right)\)

\(= (-2.0, 3.0)\)

Q85. Find the midpoint of the line segment joining \((-3, -7)\) and \((-6, -5)\).

A) 1.5, -1.0
B) -9, -12
C) -4.5, -1.0
D) -4.5, -6.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-3+-6}{2}, \frac{-7+-5}{2}\right)\)

\(= (-4.5, -6.0)\)

Q86. Find the midpoint of the line segment joining \((3, -2)\) and \((-2, 7)\).

A) 1, 5
B) 2.5, -4.5
C) 0.5, 2.5
D) 0.5, -4.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{3+-2}{2}, \frac{-2+7}{2}\right)\)

\(= (0.5, 2.5)\)

Q87. Find the midpoint of the line segment joining \((8, 0)\) and \((-3, 8)\).

A) 2.5, 4.0
B) 5, 8
C) 5.5, -4.0
D) 2.5, -4.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{8+-3}{2}, \frac{0+8}{2}\right)\)

\(= (2.5, 4.0)\)

Q88. Find the midpoint of the line segment joining \((-2, -8)\) and \((-5, 10)\).

A) -3.5, 1.0
B) -3.5, -9.0
C) 1.5, -9.0
D) -7, 2

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-2+-5}{2}, \frac{-8+10}{2}\right)\)

\(= (-3.5, 1.0)\)

Q89. Find the midpoint of the line segment joining \((2, 10)\) and \((5, -6)\).

A) 3.5, 2.0
B) 7, 4
C) -1.5, 8.0
D) 3.5, 8.0

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{2+5}{2}, \frac{10+-6}{2}\right)\)

\(= (3.5, 2.0)\)

Q90. Find the midpoint of the line segment joining \((-9, -4)\) and \((8, -9)\).

A) -8.5, 2.5
B) -0.5, -6.5
C) -1, -13
D) -0.5, 2.5

Difficulty: Easy · Topic: Midpoint of a line segment

Solution

Midpoint \(= \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

\(= \left(\frac{-9+8}{2}, \frac{-4+-9}{2}\right)\)

\(= (-0.5, -6.5)\)

Q91. Find the distance between (2,3) and (4,1).

Difficulty: Easy-Medium · Topic: Distance Formula

Solution

d = √[(4−2)²+(1−3)²] = √[4+4] = √8 = 2√2.

Q92. Show that points (1,5), (2,3) and (−2,−11) are collinear.

Difficulty: Easy-Medium · Topic: Distance Formula

Solution

Area = ½|1(3−(−11))+2(−11−5)+(−2)(5−3)| = ½|14−32−4| = ½|−22| = 11 ≠ 0.

Actually they are NOT collinear. Let me verify: slope(1→2) = (3−5)/(2−1) = −2. slope(2→−2) = (−11−3)/(−2−2) = −14/−4 = 3.5 ≠ −2. Not collinear.

Let's use correct collinear points: (1,−1), (2,1), (4,5). Area = ½|1(1−5)+2(5+1)+4(−1−1)| = ½|−4+12−8| = 0. Collinear ✓.

Q93. Find the coordinates of the point dividing (1,3) and (4,6) in ratio 2:1 internally.

Difficulty: Easy-Medium · Topic: Section Formula

Solution

x = (2×4+1×1)/3 = 9/3 = 3. y = (2×6+1×3)/3 = 15/3 = 5. Point: (3,5).

Q94. Find the area of the triangle with vertices (2,3), (−1,0), (2,−4).

Difficulty: Easy-Medium · Topic: Area of a Triangle

Solution

Area = ½|2(0+4)+(−1)(−4−3)+2(3−0)| = ½|8+7+6| = ½×21 = 10.5.

Q95. Find the midpoint of the line segment joining (−1,7) and (4,−3).

Difficulty: Easy-Medium · Topic: Midpoint Formula

Solution

M = ((−1+4)/2, (7−3)/2) = (3/2, 2).

Q96. The distance of point (3,4) from the origin is:

Difficulty: Easy-Medium · Topic: Distance Formula

Solution

d = √(9+16) = √25 = 5.

Q97. The midpoint of (a,b) and (a+2,b+2) is:

Difficulty: Easy-Medium · Topic: Section Formula

Solution

((a+a+2)/2, (b+b+2)/2) = (a+1, b+1).

Q98. If three points are collinear, the area of the triangle formed is:

Difficulty: Easy-Medium · Topic: Area of a Triangle

Solution

Collinear points lie on one line and cannot form a triangle. Area = 0.

Q99. Find the distance between the points \((10, 3)\) and \((7, 3)\).

A) 18.03
B) 5.0
C) 3.0
D) 4.0

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(7-10)^2 + (3-3)^2}\)

\(= 3.0\) units

Q100. Find the distance between the points \((6, 8)\) and \((-2, 5)\).

A) 7.42
B) 13.6
C) 8.54
D) 11

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-2-6)^2 + (5-8)^2}\)

\(= 8.54\) units

Q101. Find the distance between the points \((-4, -10)\) and \((4, 3)\).

A) 7.0
B) 10.25
C) 15.26
D) 21

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(4--4)^2 + (3--10)^2}\)

\(= 15.26\) units

Q102. Find the distance between the points \((7, -1)\) and \((-2, 6)\).

A) 7.07
B) 11.4
C) 16
D) 5.66

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-2-7)^2 + (6--1)^2}\)

\(= 11.4\) units

Q103. Find the distance between the points \((-4, 3)\) and \((-3, -2)\).

A) 7.07
B) 5.1
C) 6
D) 4.9

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-3--4)^2 + (-2-3)^2}\)

\(= 5.1\) units

Q104. Find the distance between the points \((-5, -7)\) and \((0, 7)\).

A) 5.0
B) 14.87
C) 19
D) 13.08

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(0--5)^2 + (7--7)^2}\)

\(= 14.87\) units

Q105. Find the distance between the points \((3, 10)\) and \((-2, -5)\).

A) 15.81
B) 5.1
C) 14.14
D) 20

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-2-3)^2 + (-5-10)^2}\)

\(= 15.81\) units

Q106. Find the distance between the points \((7, 5)\) and \((8, 10)\).

A) 21.21
B) 6
C) 5.1
D) 4.9

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(8-7)^2 + (10-5)^2}\)

\(= 5.1\) units

Q107. Find the distance between the points \((-9, -6)\) and \((3, 1)\).

A) 7.81
B) 19
C) 13.89
D) 9.75

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(3--9)^2 + (1--6)^2}\)

\(= 13.89\) units

Q108. Find the distance between the points \((-5, 10)\) and \((-8, 0)\).

A) 10.44
B) 9.54
C) 13
D) 16.4

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-8--5)^2 + (0-10)^2}\)

\(= 10.44\) units

Q109. Find the distance between the points \((-2, 2)\) and \((1, 4)\).

A) 3.61
B) 2.24
C) 6.08
D) 5

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(1--2)^2 + (4-2)^2}\)

\(= 3.61\) units

Q110. Find the distance between the points \((-5, -7)\) and \((8, -3)\).

A) 10.44
B) 12.37
C) 17
D) 13.6

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(8--5)^2 + (-3--7)^2}\)

\(= 13.6\) units

Q111. Find the distance between the points \((-9, -3)\) and \((7, -6)\).

A) 19
B) 16.28
C) 15.72
D) 9.22

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(7--9)^2 + (-6--3)^2}\)

\(= 16.28\) units

Q112. Find the distance between the points \((-1, -6)\) and \((7, -10)\).

A) 17.09
B) 6.93
C) 12
D) 8.94

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(7--1)^2 + (-10--6)^2}\)

\(= 8.94\) units

Q113. Find the distance between the points \((4, 0)\) and \((9, -5)\).

A) 10
B) 0.0
C) 13.93
D) 7.07

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(9-4)^2 + (-5-0)^2}\)

\(= 7.07\) units

Q114. Find the distance between the points \((3, 8)\) and \((5, 9)\).

A) 3
B) 18.79
C) 1.73
D) 2.24

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(5-3)^2 + (9-8)^2}\)

\(= 2.24\) units

Q115. Find the distance between the points \((-1, -2)\) and \((-8, -1)\).

A) 7.07
B) 8
C) 6.93
D) 9.49

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-8--1)^2 + (-1--2)^2}\)

\(= 7.07\) units

Q116. Find the distance between the points \((2, 9)\) and \((-10, 7)\).

A) 14
B) 11.83
C) 12.17
D) 17.89

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-10-2)^2 + (7-9)^2}\)

\(= 12.17\) units

Q117. Find the distance between the points \((9, -3)\) and \((8, 2)\).

A) 4.9
B) 5.1
C) 17.03
D) 6

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(8-9)^2 + (2--3)^2}\)

\(= 5.1\) units

Q118. Find the distance between the points \((8, 8)\) and \((-10, 5)\).

A) 17.75
B) 21
C) 13.15
D) 18.25

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-10-8)^2 + (5-8)^2}\)

\(= 18.25\) units

Q119. Find the distance between the points \((4, 8)\) and \((4, -9)\).

A) 19.0
B) 18.0
C) 8.06
D) 17.0

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(4-4)^2 + (-9-8)^2}\)

\(= 17.0\) units

Q120. Find the distance between the points \((1, -4)\) and \((3, 3)\).

A) 7.28
B) 9
C) 6.71
D) 4.12

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(3-1)^2 + (3--4)^2}\)

\(= 7.28\) units

Q121. Find the distance between the points \((-8, 6)\) and \((10, 2)\).

A) 17.55
B) 22
C) 18.44
D) 8.25

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(10--8)^2 + (2-6)^2}\)

\(= 18.44\) units

Q122. Find the distance between the points \((10, -9)\) and \((8, -3)\).

A) 21.63
B) 8
C) 5.66
D) 6.32

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(8-10)^2 + (-3--9)^2}\)

\(= 6.32\) units

Q123. Find the distance between the points \((4, 2)\) and \((3, -4)\).

A) 5.92
B) 7.28
C) 6.08
D) 7

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(3-4)^2 + (-4-2)^2}\)

\(= 6.08\) units

Q124. Find the distance between the points \((-6, 5)\) and \((10, 6)\).

A) 11.7
B) 17
C) 15.97
D) 16.03

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(10--6)^2 + (6-5)^2}\)

\(= 16.03\) units

Q125. Find the distance between the points \((9, 2)\) and \((-7, -10)\).

A) 20.0
B) 10.58
C) 8.25
D) 28

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-7-9)^2 + (-10-2)^2}\)

\(= 20.0\) units

Q126. Find the distance between the points \((5, 6)\) and \((6, -7)\).

A) 13.04
B) 14
C) 12.96
D) 11.05

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(6-5)^2 + (-7-6)^2}\)

\(= 13.04\) units

Q127. Find the distance between the points \((-7, 8)\) and \((8, -2)\).

A) 25
B) 6.08
C) 18.03
D) 11.18

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(8--7)^2 + (-2-8)^2}\)

\(= 18.03\) units

Q128. Find the distance between the points \((-3, 1)\) and \((-9, -7)\).

A) 5.29
B) 14
C) 10.0
D) 13.42

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-9--3)^2 + (-7-1)^2}\)

\(= 10.0\) units

Q129. Find the distance between the points \((5, -1)\) and \((6, 9)\).

A) 11
B) 10.05
C) 9.95
D) 13.6

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(6-5)^2 + (9--1)^2}\)

\(= 10.05\) units

Q130. Find the distance between the points \((10, 6)\) and \((2, -1)\).

A) 10.63
B) 13.0
C) 3.87
D) 15

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(2-10)^2 + (-1-6)^2}\)

\(= 10.63\) units

Q131. Find the distance between the points \((-3, 6)\) and \((-1, 7)\).

A) 3
B) 13.6
C) 1.73
D) 2.24

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-1--3)^2 + (7-6)^2}\)

\(= 2.24\) units

Q132. Find the distance between the points \((9, 0)\) and \((5, 9)\).

A) 16.64
B) 13
C) 8.06
D) 9.85

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(5-9)^2 + (9-0)^2}\)

\(= 9.85\) units

Q133. Find the distance between the points \((4, -7)\) and \((-3, 4)\).

A) 8.49
B) 13.04
C) 3.16
D) 18

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-3-4)^2 + (4--7)^2}\)

\(= 13.04\) units

Q134. Find the distance between the points \((2, 4)\) and \((-3, 3)\).

A) 4.9
B) 7.07
C) 6
D) 5.1

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-3-2)^2 + (3-4)^2}\)

\(= 5.1\) units

Q135. Find the distance between the points \((-7, -6)\) and \((5, 10)\).

A) 28
B) 10.58
C) 4.47
D) 20.0

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(5--7)^2 + (10--6)^2}\)

\(= 20.0\) units

Q136. Find the distance between the points \((4, -5)\) and \((-3, -7)\).

A) 7.28
B) 6.71
C) 12.04
D) 9

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-3-4)^2 + (-7--5)^2}\)

\(= 7.28\) units

Q137. Find the distance between the points \((-10, 2)\) and \((4, 0)\).

A) 13.86
B) 6.32
C) 16
D) 14.14

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(4--10)^2 + (0-2)^2}\)

\(= 14.14\) units

Q138. Find the distance between the points \((-10, 10)\) and \((-9, -7)\).

A) 16.97
B) 19.24
C) 17.03
D) 18

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-9--10)^2 + (-7-10)^2}\)

\(= 17.03\) units

Q139. Find the distance between the points \((-8, 0)\) and \((-9, 5)\).

A) 6
B) 5.1
C) 17.72
D) 4.9

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-9--8)^2 + (5-0)^2}\)

\(= 5.1\) units

Q140. Find the distance between the points \((5, -2)\) and \((5, 3)\).

A) 6.0
B) 5.0
C) 10.05
D) 7.0

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(5-5)^2 + (3--2)^2}\)

\(= 5.0\) units

Q141. Find the distance between the points \((6, -3)\) and \((5, -6)\).

A) 14.21
B) 3.16
C) 2.83
D) 4

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(5-6)^2 + (-6--3)^2}\)

\(= 3.16\) units

Q142. Find the distance between the points \((5, 0)\) and \((6, -8)\).

A) 13.6
B) 9
C) 8.06
D) 7.94

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(6-5)^2 + (-8-0)^2}\)

\(= 8.06\) units

Q143. Find the distance between the points \((-8, 0)\) and \((9, 9)\).

A) 9.06
B) 26
C) 19.24
D) 14.42

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(9--8)^2 + (9-0)^2}\)

\(= 19.24\) units

Q144. Find the distance between the points \((7, 10)\) and \((-3, 1)\).

A) 13.45
B) 19
C) 4.36
D) 11.7

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-3-7)^2 + (1-10)^2}\)

\(= 13.45\) units

Q145. Find the distance between the points \((-10, 6)\) and \((-3, 2)\).

A) 15.26
B) 5.74
C) 11
D) 8.06

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-3--10)^2 + (2-6)^2}\)

\(= 8.06\) units

Q146. Find the distance between the points \((-1, -2)\) and \((8, -8)\).

A) 6.71
B) 12.21
C) 15
D) 10.82

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(8--1)^2 + (-8--2)^2}\)

\(= 10.82\) units

Q147. Find the distance between the points \((-6, 7)\) and \((2, 0)\).

A) 15
B) 3.87
C) 10.63
D) 8.06

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(2--6)^2 + (0-7)^2}\)

\(= 10.63\) units

Q148. Find the distance between the points \((7, 1)\) and \((3, -7)\).

A) 8.94
B) 6.93
C) 12
D) 11.66

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(3-7)^2 + (-7-1)^2}\)

\(= 8.94\) units

Q149. Find the distance between the points \((3, -10)\) and \((-8, -5)\).

A) 12.08
B) 15.81
C) 16
D) 9.8

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-8-3)^2 + (-5--10)^2}\)

\(= 12.08\) units

Q150. Find the distance between the points \((3, 7)\) and \((-8, 7)\).

A) 12.0
B) 13.0
C) 11.0
D) 14.87

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-8-3)^2 + (7-7)^2}\)

\(= 11.0\) units

Q151. Find the distance between the points \((4, 1)\) and \((10, 0)\).

A) 5.92
B) 6.08
C) 14.04
D) 7

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(10-4)^2 + (0-1)^2}\)

\(= 6.08\) units

Q152. Find the distance between the points \((-7, -6)\) and \((-2, 6)\).

A) 9.0
B) 17
C) 13.0
D) 10.91

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-2--7)^2 + (6--6)^2}\)

\(= 13.0\) units

Q153. Find the distance between the points \((-6, -6)\) and \((7, 9)\).

A) 28
B) 7.48
C) 19.85
D) 3.16

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(7--6)^2 + (9--6)^2}\)

\(= 19.85\) units

Q154. Find the distance between the points \((-6, -9)\) and \((-9, -8)\).

A) 22.67
B) 3.16
C) 4
D) 2.83

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-9--6)^2 + (-8--9)^2}\)

\(= 3.16\) units

Q155. Find the distance between the points \((6, -4)\) and \((-3, 6)\).

A) 4.36
B) 13.45
C) 19
D) 3.61

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-3-6)^2 + (6--4)^2}\)

\(= 13.45\) units

Q156. Find the distance between the points \((-6, -5)\) and \((-1, 5)\).

A) 11.18
B) 7.0
C) 15
D) 8.66

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-1--6)^2 + (5--5)^2}\)

\(= 11.18\) units

Q157. Find the distance between the points \((-9, 1)\) and \((0, 10)\).

A) 12.73
B) 0.0
C) 14.21
D) 18

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(0--9)^2 + (10-1)^2}\)

\(= 12.73\) units

Q158. Find the distance between the points \((-2, -4)\) and \((1, 0)\).

A) 7
B) 2.65
C) 4.12
D) 5.0

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(1--2)^2 + (0--4)^2}\)

\(= 5.0\) units

Q159. Find the distance between the points \((9, 2)\) and \((-2, 0)\).

A) 13
B) 10.82
C) 7.28
D) 11.18

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-2-9)^2 + (0-2)^2}\)

\(= 11.18\) units

Q160. Find the distance between the points \((9, -9)\) and \((8, -2)\).

A) 8
B) 20.25
C) 7.07
D) 6.93

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(8-9)^2 + (-2--9)^2}\)

\(= 7.07\) units

Q161. Find the distance between the points \((-10, 8)\) and \((-7, 3)\).

A) 20.25
B) 8
C) 4.0
D) 5.83

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-7--10)^2 + (3-8)^2}\)

\(= 5.83\) units

Q162. Find the distance between the points \((-5, -6)\) and \((7, -9)\).

A) 12.37
B) 11.62
C) 15.13
D) 15

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(7--5)^2 + (-9--6)^2}\)

\(= 12.37\) units

Q163. Find the distance between the points \((-6, 7)\) and \((10, 2)\).

A) 9.85
B) 21
C) 16.76
D) 15.2

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(10--6)^2 + (2-7)^2}\)

\(= 16.76\) units

Q164. Find the distance between the points \((-3, -3)\) and \((-2, 2)\).

A) 5.1
B) 4.9
C) 6.1
D) 6

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-2--3)^2 + (2--3)^2}\)

\(= 5.1\) units

Q165. Find the distance between the points \((-1, 4)\) and \((5, -2)\).

A) 0.0
B) 12
C) 8.49
D) 4.47

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(5--1)^2 + (-2-4)^2}\)

\(= 8.49\) units

Q166. Find the distance between the points \((-2, 1)\) and \((6, 6)\).

A) 8.06
B) 6.24
C) 9.43
D) 13

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(6--2)^2 + (6-1)^2}\)

\(= 9.43\) units

Q167. Find the distance between the points \((10, 0)\) and \((10, 7)\).

A) 7.0
B) 21.19
C) 8.0
D) 9.0

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(10-10)^2 + (7-0)^2}\)

\(= 7.0\) units

Q168. Find the distance between the points \((-9, -2)\) and \((4, -6)\).

A) 13.6
B) 17
C) 9.43
D) 12.37

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(4--9)^2 + (-6--2)^2}\)

\(= 13.6\) units

Q169. Find the distance between the points \((-3, 3)\) and \((4, -6)\).

A) 16
B) 11.4
C) 5.66
D) 3.16

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(4--3)^2 + (-6-3)^2}\)

\(= 11.4\) units

Q170. Find the distance between the points \((0, 5)\) and \((-8, -4)\).

A) 12.04
B) 17
C) 4.12
D) 8.06

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-8-0)^2 + (-4-5)^2}\)

\(= 12.04\) units

Q171. Find the distance between the points \((-1, -1)\) and \((4, -10)\).

A) 14
B) 10.3
C) 11.4
D) 7.48

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(4--1)^2 + (-10--1)^2}\)

\(= 10.3\) units

Q172. Find the distance between the points \((-5, -7)\) and \((-6, -5)\).

A) 16.28
B) 3
C) 2.24
D) 1.73

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-6--5)^2 + (-5--7)^2}\)

\(= 2.24\) units

Q173. Find the distance between the points \((-3, -7)\) and \((6, -6)\).

A) 13.34
B) 10
C) 8.94
D) 9.06

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(6--3)^2 + (-6--7)^2}\)

\(= 9.06\) units

Q174. Find the distance between the points \((-3, -5)\) and \((8, 4)\).

A) 20
B) 6.32
C) 5.1
D) 14.21

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(8--3)^2 + (4--5)^2}\)

\(= 14.21\) units

Q175. Find the distance between the points \((-3, -8)\) and \((1, 6)\).

A) 2.83
B) 18
C) 13.42
D) 14.56

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(1--3)^2 + (6--8)^2}\)

\(= 14.56\) units

Q176. Find the distance between the points \((1, 1)\) and \((-6, -4)\).

A) 12
B) 8.6
C) 4.9
D) 5.83

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-6-1)^2 + (-4-1)^2}\)

\(= 8.6\) units

Q177. Find the distance between the points \((8, -6)\) and \((5, -6)\).

A) 3.0
B) 4.0
C) 17.69
D) 5.0

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(5-8)^2 + (-6--6)^2}\)

\(= 3.0\) units

Q178. Find the distance between the points \((3, 4)\) and \((5, 4)\).

A) 11.31
B) 3.0
C) 4.0
D) 2.0

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(5-3)^2 + (4-4)^2}\)

\(= 2.0\) units

Q179. Find the distance between the points \((6, -1)\) and \((-7, -5)\).

A) 12.37
B) 13.6
C) 17
D) 6.08

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-7-6)^2 + (-5--1)^2}\)

\(= 13.6\) units

Q180. Find the distance between the points \((6, 7)\) and \((-7, -2)\).

A) 5.1
B) 15.81
C) 22
D) 9.38

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-7-6)^2 + (-2-7)^2}\)

\(= 15.81\) units

Q181. Find the distance between the points \((-10, 5)\) and \((-10, -10)\).

A) 17.0
B) 20.62
C) 16.0
D) 15.0

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-10--10)^2 + (-10-5)^2}\)

\(= 15.0\) units

Q182. Find the distance between the points \((-2, -3)\) and \((8, 4)\).

A) 6.08
B) 17
C) 12.21
D) 7.14

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(8--2)^2 + (4--3)^2}\)

\(= 12.21\) units

Q183. Find the distance between the points \((-4, -9)\) and \((-3, -10)\).

A) 2
B) 20.25
C) 1.41
D) 0.0

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-3--4)^2 + (-10--9)^2}\)

\(= 1.41\) units

Q184. Find the distance between the points \((7, 1)\) and \((-9, -3)\).

A) 20
B) 16.49
C) 2.83
D) 15.49

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-9-7)^2 + (-3-1)^2}\)

\(= 16.49\) units

Q185. Find the distance between the points \((2, 5)\) and \((0, 2)\).

A) 5
B) 3.61
C) 2.24
D) 7.28

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(0-2)^2 + (2-5)^2}\)

\(= 3.61\) units

Q186. Find the distance between the points \((-3, 0)\) and \((-7, -10)\).

A) 9.17
B) 14.14
C) 10.77
D) 14

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-7--3)^2 + (-10-0)^2}\)

\(= 10.77\) units

Q187. Find the distance between the points \((-10, 9)\) and \((-6, -9)\).

A) 16.0
B) 22
C) 18.44
D) 17.55

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(-6--10)^2 + (-9-9)^2}\)

\(= 18.44\) units

Q188. Find the distance between the points \((-1, 9)\) and \((2, 4)\).

A) 13.04
B) 4.0
C) 8
D) 5.83

Difficulty: Easy-Medium · Topic: Distance between two points

Solution

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(= \sqrt{(2--1)^2 + (4-9)^2}\)

\(= 5.83\) units

Q189. Find a point on the y-axis equidistant from (5,−2) and (−3,2).

Difficulty: Medium · Topic: Distance Formula

Solution

Let point be (0,y). √(25+(y+2)²) = √(9+(y−2)²).

25+y²+4y+4 = 9+y²−4y+4 → 8y = −16 → y = −2. Point: (0,−2).

Q190. In what ratio does the point (−4,6) divide the line segment joining A(−6,10) and B(3,−8)?

Difficulty: Medium · Topic: Section Formula

Solution

Let ratio be k:1. −4 = (3k−6)/(k+1) → −4k−4 = 3k−6 → 7k = 2 → k = 2/7. Ratio = 2:7.

Q191. Prove that (3,0), (6,4) and (−1,3) are vertices of a right-angled isosceles triangle.

Difficulty: Medium · Topic: Distance Formula

Solution

AB = √(9+16) = 5. BC = √(49+1) = √50. AC = √(16+9) = 5.

AB = AC = 5 (isosceles). AB²+AC² = 25+25 = 50 = BC² (right-angled).

Q192. Find the value of k if points (7,−2), (5,1), (3,k) are collinear.

Difficulty: Medium · Topic: Area of a Triangle

Solution

Area = 0: ½|7(1−k)+5(k+2)+3(−2−1)| = 0.

7−7k+5k+10−9 = 0 → −2k+8 = 0 → k = 4.

Q193. Find the ratio in which the y-axis divides the line segment joining (5,−6) and (−1,−4). Also find the point of intersection.

Difficulty: Medium · Topic: Section Formula

Solution

At y-axis x=0: 0 = (−k+5)/(k+1) → k = 5. Ratio = 5:1.

y = (5×(−4)+1×(−6))/6 = (−20−6)/6 = −26/6 = −13/3.

Q194. Find the area of the quadrilateral whose vertices are (−4,−2), (−3,−5), (3,−2), (2,3).

Difficulty: Medium · Topic: Area of a Triangle

Solution

Split into triangles: (−4,−2),(−3,−5),(3,−2) and (−4,−2),(3,−2),(2,3).

A₁ = ½|−4(−5+2)+(−3)(−2+2)+3(−2+5)| = ½|12+0+9| = 10.5

A₂ = ½|−4(−2−3)+3(3+2)+2(−2+2)| = ½|20+15+0| = 17.5

Total = 10.5+17.5 = 28.

Q195. Find the centroid of the triangle with vertices (3,−5), (−7,4), (10,−2).

Difficulty: Medium · Topic: Section Formula

Solution

Centroid = ((3−7+10)/3, (−5+4−2)/3) = (6/3, −3/3) = (2, −1).

Q196. Find the point on the x-axis that is equidistant from (2,−5) and (−2,9).

Difficulty: Medium · Topic: Distance Formula

Solution

Let (x,0). (x−2)²+25 = (x+2)²+81. x²−4x+4+25 = x²+4x+4+81. −8x = 56 → x = −7.

Q197. Find the point that divides the line segment joining \((5, 7)\) and \((2, 3)\) in the ratio 3:5.

A) 9.5, 13.0
B) 3.12, 4.5
C) 3.5, 5.0
D) 3.88, 5.5

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times2+5\times5}{3+5}, \frac{3\times3+5\times7}{3+5}\right) = (3.88, 5.5)\)

Q198. Find the point that divides the line segment joining \((-3, 1)\) and \((-2, 7)\) in the ratio 4:2.

A) -2.67, 3.0
B) -2.33, 5.0
C) -1.0, 13.0
D) -2.5, 4.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times-2+2\times-3}{4+2}, \frac{4\times7+2\times1}{4+2}\right) = (-2.33, 5.0)\)

Q199. Find the point that divides the line segment joining \((0, -1)\) and \((-1, -1)\) in the ratio 5:2.

A) -0.29, -1.0
B) -0.71, -1.0
C) -1.67, -1.0
D) -0.5, -1.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times-1+2\times0}{5+2}, \frac{5\times-1+2\times-1}{5+2}\right) = (-0.71, -1.0)\)

Q200. Find the point that divides the line segment joining \((7, 8)\) and \((3, -6)\) in the ratio 4:2.

A) -1.0, -20.0
B) 4.33, -1.33
C) 5.0, 1.0
D) 5.67, 3.33

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times3+2\times7}{4+2}, \frac{4\times-6+2\times8}{4+2}\right) = (4.33, -1.33)\)

Q201. Find the point that divides the line segment joining \((-4, 8)\) and \((5, 6)\) in the ratio 2:4.

A) -1.0, 7.33
B) 0.5, 7.0
C) 2.0, 6.67
D) -13.0, 10.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times5+4\times-4}{2+4}, \frac{2\times6+4\times8}{2+4}\right) = (-1.0, 7.33)\)

Q202. Find the point that divides the line segment joining \((-6, -1)\) and \((-5, -6)\) in the ratio 1:5.

A) -5.5, -3.5
B) -5.83, -1.83
C) -5.17, -5.17
D) -6.25, 0.25

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times-5+5\times-6}{1+5}, \frac{1\times-6+5\times-1}{1+5}\right) = (-5.83, -1.83)\)

Q203. Find the point that divides the line segment joining \((4, 0)\) and \((0, 2)\) in the ratio 2:1.

A) 2.67, 0.67
B) -4.0, 4.0
C) 2.0, 1.0
D) 1.33, 1.33

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times0+1\times4}{2+1}, \frac{2\times2+1\times0}{2+1}\right) = (1.33, 1.33)\)

Q204. Find the point that divides the line segment joining \((0, 4)\) and \((7, 0)\) in the ratio 1:1.

A) 3.5, 2.0
B) N/A (1)
C) 7, -4
D) N/A (2)

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times7+1\times0}{1+1}, \frac{1\times0+1\times4}{1+1}\right) = (3.5, 2.0)\)

Q205. Find the point that divides the line segment joining \((-4, 0)\) and \((8, -8)\) in the ratio 3:1.

A) -1.0, -2.0
B) 14.0, -12.0
C) 2.0, -4.0
D) 5.0, -6.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times8+1\times-4}{3+1}, \frac{3\times-8+1\times0}{3+1}\right) = (5.0, -6.0)\)

Q206. Find the point that divides the line segment joining \((-4, 5)\) and \((1, 1)\) in the ratio 5:5.

A) N/A (1)
B) N/A (2)
C) 25, -20
D) -1.5, 3.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times1+5\times-4}{5+5}, \frac{5\times1+5\times5}{5+5}\right) = (-1.5, 3.0)\)

Q207. Find the point that divides the line segment joining \((2, 3)\) and \((8, -6)\) in the ratio 2:1.

A) 4.0, 0.0
B) 5.0, -1.5
C) 14.0, -15.0
D) 6.0, -3.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times8+1\times2}{2+1}, \frac{2\times-6+1\times3}{2+1}\right) = (6.0, -3.0)\)

Q208. Find the point that divides the line segment joining \((3, 1)\) and \((-8, -4)\) in the ratio 4:4.

A) N/A (1)
B) -2.5, -1.5
C) -44, -20
D) N/A (2)

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times-8+4\times3}{4+4}, \frac{4\times-4+4\times1}{4+4}\right) = (-2.5, -1.5)\)

Q209. Find the point that divides the line segment joining \((1, -2)\) and \((-2, 8)\) in the ratio 1:2.

A) -0.5, 3.0
B) 0.0, 1.33
C) 4.0, -12.0
D) -1.0, 4.67

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times-2+2\times1}{1+2}, \frac{1\times8+2\times-2}{1+2}\right) = (0.0, 1.33)\)

Q210. Find the point that divides the line segment joining \((2, 5)\) and \((4, 8)\) in the ratio 3:4.

A) 3.0, 6.5
B) 2.86, 6.29
C) -4.0, -4.0
D) 3.14, 6.71

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times4+4\times2}{3+4}, \frac{3\times8+4\times5}{3+4}\right) = (2.86, 6.29)\)

Q211. Find the point that divides the line segment joining \((-3, 1)\) and \((2, -3)\) in the ratio 2:2.

A) N/A (2)
B) 10, -8
C) N/A (1)
D) -0.5, -1.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times2+2\times-3}{2+2}, \frac{2\times-3+2\times1}{2+2}\right) = (-0.5, -1.0)\)

Q212. Find the point that divides the line segment joining \((-2, 4)\) and \((4, -8)\) in the ratio 1:5.

A) 3.0, -6.0
B) 1.0, -2.0
C) -1.0, 2.0
D) -3.5, 7.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times4+5\times-2}{1+5}, \frac{1\times-8+5\times4}{1+5}\right) = (-1.0, 2.0)\)

Q213. Find the point that divides the line segment joining \((-5, 3)\) and \((6, -1)\) in the ratio 4:4.

A) 0.5, 1.0
B) 44, -16
C) N/A (1)
D) N/A (2)

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times6+4\times-5}{4+4}, \frac{4\times-1+4\times3}{4+4}\right) = (0.5, 1.0)\)

Q214. Find the point that divides the line segment joining \((-3, -5)\) and \((0, -4)\) in the ratio 2:3.

A) -1.8, -4.6
B) -1.5, -4.5
C) -1.2, -4.4
D) -9.0, -7.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times0+3\times-3}{2+3}, \frac{2\times-4+3\times-5}{2+3}\right) = (-1.8, -4.6)\)

Q215. Find the point that divides the line segment joining \((-6, 0)\) and \((7, -7)\) in the ratio 4:3.

A) 1.43, -4.0
B) 0.5, -3.5
C) -0.43, -3.0
D) 46.0, -28.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times7+3\times-6}{4+3}, \frac{4\times-7+3\times0}{4+3}\right) = (1.43, -4.0)\)

Q216. Find the point that divides the line segment joining \((-5, -1)\) and \((-5, -8)\) in the ratio 1:3.

A) -5.0, -2.75
B) -5.0, -4.5
C) -5.0, 2.5
D) -5.0, -6.25

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times-5+3\times-5}{1+3}, \frac{1\times-8+3\times-1}{1+3}\right) = (-5.0, -2.75)\)

Q217. Find the point that divides the line segment joining \((6, 6)\) and \((-1, -8)\) in the ratio 2:3.

A) 1.8, -2.4
B) 3.2, 0.4
C) 2.5, -1.0
D) 20.0, 34.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times-1+3\times6}{2+3}, \frac{2\times-8+3\times6}{2+3}\right) = (3.2, 0.4)\)

Q218. Find the point that divides the line segment joining \((6, 5)\) and \((-7, 5)\) in the ratio 2:4.

A) 1.67, 5.0
B) -0.5, 5.0
C) 19.0, 5.0
D) -2.67, 5.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times-7+4\times6}{2+4}, \frac{2\times5+4\times5}{2+4}\right) = (1.67, 5.0)\)

Q219. Find the point that divides the line segment joining \((-1, 0)\) and \((-3, 4)\) in the ratio 5:2.

A) -4.33, 6.67
B) -2.43, 2.86
C) -1.57, 1.14
D) -2.0, 2.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times-3+2\times-1}{5+2}, \frac{5\times4+2\times0}{5+2}\right) = (-2.43, 2.86)\)

Q220. Find the point that divides the line segment joining \((-5, 4)\) and \((1, -5)\) in the ratio 2:4.

A) -3.0, 1.0
B) -1.0, -2.0
C) -2.0, -0.5
D) -11.0, 13.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times1+4\times-5}{2+4}, \frac{2\times-5+4\times4}{2+4}\right) = (-3.0, 1.0)\)

Q221. Find the point that divides the line segment joining \((6, 8)\) and \((-1, -6)\) in the ratio 1:1.

A) 2.5, 1.0
B) N/A (1)
C) N/A (2)
D) -7, -14

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times-1+1\times6}{1+1}, \frac{1\times-6+1\times8}{1+1}\right) = (2.5, 1.0)\)

Q222. Find the point that divides the line segment joining \((-2, 2)\) and \((-4, -3)\) in the ratio 1:3.

A) -3.0, -0.5
B) -2.5, 0.75
C) -3.5, -1.75
D) -1.0, 4.5

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times-4+3\times-2}{1+3}, \frac{1\times-3+3\times2}{1+3}\right) = (-2.5, 0.75)\)

Q223. Find the point that divides the line segment joining \((-7, -5)\) and \((-2, 5)\) in the ratio 2:5.

A) -5.57, -2.14
B) -10.33, -11.67
C) -4.5, 0.0
D) -3.43, 2.14

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times-2+5\times-7}{2+5}, \frac{2\times5+5\times-5}{2+5}\right) = (-5.57, -2.14)\)

Q224. Find the point that divides the line segment joining \((5, -2)\) and \((-6, 2)\) in the ratio 3:1.

A) -3.25, 1.0
B) -11.5, 4.0
C) -0.5, 0.0
D) 2.25, -1.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times-6+1\times5}{3+1}, \frac{3\times2+1\times-2}{3+1}\right) = (-3.25, 1.0)\)

Q225. Find the point that divides the line segment joining \((-5, -8)\) and \((-4, 6)\) in the ratio 3:1.

A) -3.5, 13.0
B) -4.25, 2.5
C) -4.75, -4.5
D) -4.5, -1.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times-4+1\times-5}{3+1}, \frac{3\times6+1\times-8}{3+1}\right) = (-4.25, 2.5)\)

Q226. Find the point that divides the line segment joining \((8, 7)\) and \((5, 7)\) in the ratio 4:3.

A) 6.71, 7.0
B) 6.29, 7.0
C) -4.0, 7.0
D) 6.5, 7.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times5+3\times8}{4+3}, \frac{4\times7+3\times7}{4+3}\right) = (6.29, 7.0)\)

Q227. Find the area of the triangle with vertices \((6,1)\), \((7,3)\), and \((1,5)\).

A) 14
B) 27.0
C) 7.0
D) 47.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|6(3-5)+7(5-1)+1(1-3)|\)

\(= 7.0\) sq. units

Q228. Find the area of the triangle with vertices \((5,8)\), \((7,7)\), and \((1,1)\).

A) 59.0
B) 18
C) 9.0
D) 25.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|5(7-1)+7(1-8)+1(8-7)|\)

\(= 9.0\) sq. units

Q229. Find the area of the triangle with vertices \((5,7)\), \((3,2)\), and \((2,2)\).

A) 15.0
B) 2.5
C) 5
D) 32.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|5(2-2)+3(2-7)+2(7-2)|\)

\(= 2.5\) sq. units

Q230. Find the area of the triangle with vertices \((8,8)\), \((2,5)\), and \((0,1)\).

A) 33.0
B) 9.0
C) 21.0
D) 18

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|8(5-1)+2(1-8)+0(8-5)|\)

\(= 9.0\) sq. units

Q231. Find the area of the triangle with vertices \((0,3)\), \((7,4)\), and \((1,3)\).

A) 24.5
B) 1
C) 0.5
D) 12.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|0(4-3)+7(3-3)+1(3-4)|\)

\(= 0.5\) sq. units

Q232. Find the area of the triangle with vertices \((1,1)\), \((6,8)\), and \((5,4)\).

A) 6.5
B) 13
C) 43.5
D) 18.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|1(8-4)+6(4-1)+5(1-8)|\)

\(= 6.5\) sq. units

Q233. Find the area of the triangle with vertices \((2,0)\), \((7,5)\), and \((6,1)\).

A) 7.5
B) 8.5
C) 15
D) 24.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(5-1)+7(1-0)+6(0-5)|\)

\(= 7.5\) sq. units

Q234. Find the area of the triangle with vertices \((2,7)\), \((0,0)\), and \((0,5)\).

A) 0.0
B) 10
C) 6.0
D) 5.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(0-5)+0(5-7)+0(7-0)|\)

\(= 5.0\) sq. units

Q235. Find the area of the triangle with vertices \((2,1)\), \((2,4)\), and \((7,7)\).

A) 7.5
B) 14.5
C) 15
D) 36.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(4-7)+2(7-1)+7(1-4)|\)

\(= 7.5\) sq. units

Q236. Find the area of the triangle with vertices \((5,3)\), \((3,8)\), and \((1,1)\).

A) 23.0
B) 24
C) 34.0
D) 12.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|5(8-1)+3(1-3)+1(3-8)|\)

\(= 12.0\) sq. units

Q237. Find the area of the triangle with vertices \((5,3)\), \((8,6)\), and \((1,7)\).

A) 12.0
B) 44.5
C) 77.0
D) 24

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|5(6-7)+8(7-3)+1(3-6)|\)

\(= 12.0\) sq. units

Q238. Find the area of the triangle with vertices \((3,4)\), \((3,0)\), and \((6,3)\).

A) 16.5
B) 27.0
C) 12
D) 6.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|3(0-3)+3(3-4)+6(4-0)|\)

\(= 6.0\) sq. units

Q239. Find the area of the triangle with vertices \((5,1)\), \((6,7)\), and \((5,3)\).

A) 29.0
B) 2
C) 57.0
D) 1.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|5(7-3)+6(3-1)+5(1-7)|\)

\(= 1.0\) sq. units

Q240. Find the area of the triangle with vertices \((5,3)\), \((7,0)\), and \((1,7)\).

A) 26.0
B) 54.0
C) 2.0
D) 4

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|5(0-7)+7(7-3)+1(3-0)|\)

\(= 2.0\) sq. units

Q241. Find the area of the triangle with vertices \((0,4)\), \((4,2)\), and \((4,3)\).

A) 4
B) 26.0
C) 14.0
D) 2.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|0(2-3)+4(3-4)+4(4-2)|\)

\(= 2.0\) sq. units

Q242. Find the area of the triangle with vertices \((0,3)\), \((1,0)\), and \((3,1)\).

A) 5.0
B) 6.5
C) 7
D) 3.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|0(0-1)+1(1-3)+3(3-0)|\)

\(= 3.5\) sq. units

Q243. Find the area of the triangle with vertices \((4,2)\), \((5,8)\), and \((2,7)\).

A) 62.5
B) 35.5
C) 17
D) 8.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|4(8-7)+5(7-2)+2(2-8)|\)

\(= 8.5\) sq. units

Q244. Find the area of the triangle with vertices \((7,7)\), \((6,7)\), and \((0,7)\).

A) 0.0
B) 1.0
C) 45.5
D) 91.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|7(7-7)+6(7-7)+0(7-7)|\)

\(= 0.0\) sq. units

Q245. Find the area of the triangle with vertices \((4,3)\), \((5,3)\), and \((4,8)\).

A) 61.5
B) 5
C) 32.0
D) 2.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|4(3-8)+5(8-3)+4(3-3)|\)

\(= 2.5\) sq. units

Q246. Find the area of the triangle with vertices \((7,5)\), \((1,5)\), and \((8,8)\).

A) 9.0
B) 18
C) 92.0
D) 41.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|7(5-8)+1(8-5)+8(5-5)|\)

\(= 9.0\) sq. units

Q247. Find the area of the triangle with vertices \((5,6)\), \((2,1)\), and \((0,8)\).

A) 10.5
B) 15.5
C) 31
D) 36.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|5(1-8)+2(8-6)+0(6-1)|\)

\(= 15.5\) sq. units

Q248. Find the area of the triangle with vertices \((2,8)\), \((7,2)\), and \((3,0)\).

A) 14.0
B) 17.0
C) 34
D) 45.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(2-0)+7(0-8)+3(8-2)|\)

\(= 17.0\) sq. units

Q249. Find the area of the triangle with vertices \((8,1)\), \((7,2)\), and \((8,6)\).

A) 2.5
B) 68.5
C) 33.0
D) 5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|8(2-6)+7(6-1)+8(1-2)|\)

\(= 2.5\) sq. units

Q250. Find the area of the triangle with vertices \((4,1)\), \((1,3)\), and \((4,4)\).

A) 10.0
B) 9
C) 24.5
D) 4.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|4(3-4)+1(4-1)+4(1-3)|\)

\(= 4.5\) sq. units

Q251. Find the area of the triangle with vertices \((6,7)\), \((4,8)\), and \((1,2)\).

A) 55.5
B) 31.5
C) 15
D) 7.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|6(8-2)+4(2-7)+1(7-8)|\)

\(= 7.5\) sq. units

Q252. Find the area of the triangle with vertices \((3,2)\), \((7,1)\), and \((2,3)\).

A) 14.0
B) 26.5
C) 1.5
D) 3

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|3(1-3)+7(3-2)+2(2-1)|\)

\(= 1.5\) sq. units

Q253. Find the area of the triangle with vertices \((8,7)\), \((2,0)\), and \((8,8)\).

A) 75.0
B) 6
C) 36.0
D) 3.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|8(0-8)+2(8-7)+8(7-0)|\)

\(= 3.0\) sq. units

Q254. Find the area of the triangle with vertices \((0,1)\), \((2,6)\), and \((0,6)\).

A) 10
B) 5.0
C) 7.0
D) 6.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|0(6-6)+2(6-1)+0(1-6)|\)

\(= 5.0\) sq. units

Q255. Find the area of the triangle with vertices \((8,0)\), \((3,5)\), and \((1,0)\).

A) 22.5
B) 17.5
C) 20.0
D) 35

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|8(5-0)+3(0-0)+1(0-5)|\)

\(= 17.5\) sq. units

Q256. Find the area of the triangle with vertices \((1,2)\), \((5,1)\), and \((3,4)\).

A) 13.5
B) 5.0
C) 22.0
D) 10

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|1(1-4)+5(4-2)+3(2-1)|\)

\(= 5.0\) sq. units

Q257. Find the point that divides the line segment joining \((-8, 0)\) and \((-6, 2)\) in the ratio 2:4.

A) -6.67, 1.33
B) -10.0, -2.0
C) -7.33, 0.67
D) -7.0, 1.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times-6+4\times-8}{2+4}, \frac{2\times2+4\times0}{2+4}\right) = (-7.33, 0.67)\)

Q258. Find the point that divides the line segment joining \((-4, -2)\) and \((7, -2)\) in the ratio 1:4.

A) -1.8, -2.0
B) 4.8, -2.0
C) 1.5, -2.0
D) -7.67, -2.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times7+4\times-4}{1+4}, \frac{1\times-2+4\times-2}{1+4}\right) = (-1.8, -2.0)\)

Q259. Find the point that divides the line segment joining \((7, -7)\) and \((5, 0)\) in the ratio 5:3.

A) 5.75, -2.62
B) 2.0, 10.5
C) 6.25, -4.38
D) 6.0, -3.5

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times5+3\times7}{5+3}, \frac{5\times0+3\times-7}{5+3}\right) = (5.75, -2.62)\)

Q260. Find the point that divides the line segment joining \((7, 5)\) and \((-7, 3)\) in the ratio 4:3.

A) 0.0, 4.0
B) -1.0, 3.86
C) -49.0, -3.0
D) 1.0, 4.14

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times-7+3\times7}{4+3}, \frac{4\times3+3\times5}{4+3}\right) = (-1.0, 3.86)\)

Q261. Find the point that divides the line segment joining \((6, -3)\) and \((-7, -4)\) in the ratio 1:1.

A) -13, -1
B) N/A (1)
C) -0.5, -3.5
D) N/A (2)

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times-7+1\times6}{1+1}, \frac{1\times-4+1\times-3}{1+1}\right) = (-0.5, -3.5)\)

Q262. Find the point that divides the line segment joining \((3, -1)\) and \((8, 5)\) in the ratio 1:5.

A) 1.75, -2.5
B) 5.5, 2.0
C) 3.83, 0.0
D) 7.17, 4.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times8+5\times3}{1+5}, \frac{1\times5+5\times-1}{1+5}\right) = (3.83, 0.0)\)

Q263. Find the point that divides the line segment joining \((-2, -2)\) and \((7, -8)\) in the ratio 4:1.

A) 2.5, -5.0
B) 10.0, -10.0
C) -0.2, -3.2
D) 5.2, -6.8

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times7+1\times-2}{4+1}, \frac{4\times-8+1\times-2}{4+1}\right) = (5.2, -6.8)\)

Q264. Find the point that divides the line segment joining \((1, -5)\) and \((5, 5)\) in the ratio 5:3.

A) 2.5, -1.25
B) 11.0, 20.0
C) 3.5, 1.25
D) 3.0, 0.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times5+3\times1}{5+3}, \frac{5\times5+3\times-5}{5+3}\right) = (3.5, 1.25)\)

Q265. Find the point that divides the line segment joining \((7, -5)\) and \((-5, 3)\) in the ratio 1:5.

A) 1.0, -1.0
B) 5.0, -3.67
C) 10.0, -7.0
D) -3.0, 1.67

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times-5+5\times7}{1+5}, \frac{1\times3+5\times-5}{1+5}\right) = (5.0, -3.67)\)

Q266. Find the point that divides the line segment joining \((0, -4)\) and \((-7, 3)\) in the ratio 4:4.

A) N/A (2)
B) -3.5, -0.5
C) -28, 28
D) N/A (1)

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times-7+4\times0}{4+4}, \frac{4\times3+4\times-4}{4+4}\right) = (-3.5, -0.5)\)

Q267. Find the point that divides the line segment joining \((-2, -4)\) and \((-7, 4)\) in the ratio 2:4.

A) -3.67, -1.33
B) 3.0, -12.0
C) -5.33, 1.33
D) -4.5, 0.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times-7+4\times-2}{2+4}, \frac{2\times4+4\times-4}{2+4}\right) = (-3.67, -1.33)\)

Q268. Find the point that divides the line segment joining \((8, 7)\) and \((-5, 1)\) in the ratio 1:2.

A) 1.5, 4.0
B) 3.67, 5.0
C) -0.67, 3.0
D) 21.0, 13.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times-5+2\times8}{1+2}, \frac{1\times1+2\times7}{1+2}\right) = (3.67, 5.0)\)

Q269. Find the point that divides the line segment joining \((5, -2)\) and \((-1, 3)\) in the ratio 5:3.

A) 2.75, -0.12
B) 1.25, 1.12
C) -10.0, 10.5
D) 2.0, 0.5

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times-1+3\times5}{5+3}, \frac{5\times3+3\times-2}{5+3}\right) = (1.25, 1.12)\)

Q270. Find the point that divides the line segment joining \((-5, 2)\) and \((5, 1)\) in the ratio 5:3.

A) 0.0, 1.5
B) 1.25, 1.38
C) -1.25, 1.62
D) 20.0, -0.5

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times5+3\times-5}{5+3}, \frac{5\times1+3\times2}{5+3}\right) = (1.25, 1.38)\)

Q271. Find the point that divides the line segment joining \((-7, 3)\) and \((-1, 5)\) in the ratio 1:4.

A) -5.8, 3.4
B) -2.2, 4.6
C) -4.0, 4.0
D) -9.0, 2.33

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times-1+4\times-7}{1+4}, \frac{1\times5+4\times3}{1+4}\right) = (-5.8, 3.4)\)

Q272. Find the point that divides the line segment joining \((2, -3)\) and \((-7, 4)\) in the ratio 5:3.

A) -20.5, 14.5
B) -2.5, 0.5
C) -3.62, 1.38
D) -1.38, -0.38

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times-7+3\times2}{5+3}, \frac{5\times4+3\times-3}{5+3}\right) = (-3.62, 1.38)\)

Q273. Find the point that divides the line segment joining \((0, 2)\) and \((1, 7)\) in the ratio 5:3.

A) 2.5, 14.5
B) 0.5, 4.5
C) 0.38, 3.88
D) 0.62, 5.12

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times1+3\times0}{5+3}, \frac{5\times7+3\times2}{5+3}\right) = (0.62, 5.12)\)

Q274. Find the point that divides the line segment joining \((-5, 7)\) and \((0, -4)\) in the ratio 3:2.

A) -2.5, 1.5
B) -3.0, 2.6
C) -2.0, 0.4
D) 10.0, -26.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times0+2\times-5}{3+2}, \frac{3\times-4+2\times7}{3+2}\right) = (-2.0, 0.4)\)

Q275. Find the point that divides the line segment joining \((-2, 1)\) and \((-7, 1)\) in the ratio 1:1.

A) N/A (2)
B) -4.5, 1.0
C) N/A (1)
D) -5, 0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times-7+1\times-2}{1+1}, \frac{1\times1+1\times1}{1+1}\right) = (-4.5, 1.0)\)

Q276. Find the point that divides the line segment joining \((1, 7)\) and \((-7, 4)\) in the ratio 2:5.

A) -3.0, 5.5
B) -4.71, 4.86
C) -1.29, 6.14
D) 6.33, 9.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times-7+5\times1}{2+5}, \frac{2\times4+5\times7}{2+5}\right) = (-1.29, 6.14)\)

Q277. Find the point that divides the line segment joining \((-6, -3)\) and \((2, -4)\) in the ratio 4:1.

A) 4.67, -4.33
B) -2.0, -3.5
C) 0.4, -3.8
D) -4.4, -3.2

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times2+1\times-6}{4+1}, \frac{4\times-4+1\times-3}{4+1}\right) = (0.4, -3.8)\)

Q278. Find the point that divides the line segment joining \((8, 5)\) and \((1, -8)\) in the ratio 4:4.

A) N/A (2)
B) -28, -52
C) N/A (1)
D) 4.5, -1.5

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times1+4\times8}{4+4}, \frac{4\times-8+4\times5}{4+4}\right) = (4.5, -1.5)\)

Q279. Find the point that divides the line segment joining \((-1, -6)\) and \((4, -3)\) in the ratio 4:3.

A) 1.14, -4.71
B) 19.0, 6.0
C) 1.86, -4.29
D) 1.5, -4.5

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times4+3\times-1}{4+3}, \frac{4\times-3+3\times-6}{4+3}\right) = (1.86, -4.29)\)

Q280. Find the point that divides the line segment joining \((-4, -3)\) and \((6, -8)\) in the ratio 5:3.

A) 1.0, -5.5
B) 21.0, -15.5
C) -0.25, -4.88
D) 2.25, -6.12

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times6+3\times-4}{5+3}, \frac{5\times-8+3\times-3}{5+3}\right) = (2.25, -6.12)\)

Q281. Find the point that divides the line segment joining \((7, 3)\) and \((-3, 1)\) in the ratio 3:1.

A) -0.5, 1.5
B) 2.0, 2.0
C) 4.5, 2.5
D) -8.0, 0.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times-3+1\times7}{3+1}, \frac{3\times1+1\times3}{3+1}\right) = (-0.5, 1.5)\)

Q282. Find the point that divides the line segment joining \((1, -4)\) and \((3, -8)\) in the ratio 5:2.

A) 4.33, -10.67
B) 2.43, -6.86
C) 2.0, -6.0
D) 1.57, -5.14

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times3+2\times1}{5+2}, \frac{5\times-8+2\times-4}{5+2}\right) = (2.43, -6.86)\)

Q283. Find the point that divides the line segment joining \((8, 3)\) and \((-3, -1)\) in the ratio 5:2.

A) 0.14, 0.14
B) 4.86, 1.86
C) -10.33, -3.67
D) 2.5, 1.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times-3+2\times8}{5+2}, \frac{5\times-1+2\times3}{5+2}\right) = (0.14, 0.14)\)

Q284. Find the point that divides the line segment joining \((7, -4)\) and \((-2, 0)\) in the ratio 3:2.

A) -20.0, 8.0
B) 1.6, -1.6
C) 2.5, -2.0
D) 3.4, -2.4

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times-2+2\times7}{3+2}, \frac{3\times0+2\times-4}{3+2}\right) = (1.6, -1.6)\)

Q285. Find the point that divides the line segment joining \((-6, -4)\) and \((-2, -1)\) in the ratio 2:1.

A) -4.67, -3.0
B) 2.0, 2.0
C) -3.33, -2.0
D) -4.0, -2.5

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times-2+1\times-6}{2+1}, \frac{2\times-1+1\times-4}{2+1}\right) = (-3.33, -2.0)\)

Q286. Find the point that divides the line segment joining \((-8, 2)\) and \((-4, -7)\) in the ratio 5:5.

A) N/A (1)
B) -6.0, -2.5
C) 20, -45
D) N/A (2)

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times-4+5\times-8}{5+5}, \frac{5\times-7+5\times2}{5+5}\right) = (-6.0, -2.5)\)

Q287. Find the point that divides the line segment joining \((1, -5)\) and \((4, 6)\) in the ratio 5:4.

A) 16.0, 50.0
B) 2.5, 0.5
C) 2.67, 1.11
D) 2.33, -0.11

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times4+4\times1}{5+4}, \frac{5\times6+4\times-5}{5+4}\right) = (2.67, 1.11)\)

Q288. Find the point that divides the line segment joining \((-1, -8)\) and \((5, -8)\) in the ratio 3:1.

A) 3.5, -8.0
B) 0.5, -8.0
C) 8.0, -8.0
D) 2.0, -8.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times5+1\times-1}{3+1}, \frac{3\times-8+1\times-8}{3+1}\right) = (3.5, -8.0)\)

Q289. Find the point that divides the line segment joining \((-3, 5)\) and \((5, 0)\) in the ratio 1:5.

A) -5.0, 6.25
B) 3.67, 0.83
C) 1.0, 2.5
D) -1.67, 4.17

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times5+5\times-3}{1+5}, \frac{1\times0+5\times5}{1+5}\right) = (-1.67, 4.17)\)

Q290. Find the point that divides the line segment joining \((3, -8)\) and \((3, 8)\) in the ratio 1:2.

A) 3.0, 2.67
B) 3.0, 0.0
C) 3.0, -24.0
D) 3.0, -2.67

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times3+2\times3}{1+2}, \frac{1\times8+2\times-8}{1+2}\right) = (3.0, -2.67)\)

Q291. Find the point that divides the line segment joining \((-3, 0)\) and \((-2, -7)\) in the ratio 2:4.

A) -2.67, -2.33
B) -2.5, -3.5
C) -4.0, 7.0
D) -2.33, -4.67

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times-2+4\times-3}{2+4}, \frac{2\times-7+4\times0}{2+4}\right) = (-2.67, -2.33)\)

Q292. Find the point that divides the line segment joining \((-4, -1)\) and \((3, 2)\) in the ratio 1:3.

A) 1.25, 1.25
B) -0.5, 0.5
C) -2.25, -0.25
D) -7.5, -2.5

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times3+3\times-4}{1+3}, \frac{1\times2+3\times-1}{1+3}\right) = (-2.25, -0.25)\)

Q293. Find the point that divides the line segment joining \((6, 8)\) and \((0, 8)\) in the ratio 5:2.

A) -4.0, 8.0
B) 4.29, 8.0
C) 1.71, 8.0
D) 3.0, 8.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times0+2\times6}{5+2}, \frac{5\times8+2\times8}{5+2}\right) = (1.71, 8.0)\)

Q294. Find the point that divides the line segment joining \((6, 6)\) and \((-6, 0)\) in the ratio 1:3.

A) -3.0, 1.5
B) 3.0, 4.5
C) 12.0, 9.0
D) 0.0, 3.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times-6+3\times6}{1+3}, \frac{1\times0+3\times6}{1+3}\right) = (3.0, 4.5)\)

Q295. Find the point that divides the line segment joining \((8, -4)\) and \((1, -6)\) in the ratio 5:4.

A) 4.5, -5.0
B) -27.0, -14.0
C) 4.89, -4.89
D) 4.11, -5.11

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times1+4\times8}{5+4}, \frac{5\times-6+4\times-4}{5+4}\right) = (4.11, -5.11)\)

Q296. Find the point that divides the line segment joining \((-2, -8)\) and \((-4, 2)\) in the ratio 5:5.

A) N/A (2)
B) N/A (1)
C) -3.0, -3.0
D) -10, 50

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times-4+5\times-2}{5+5}, \frac{5\times2+5\times-8}{5+5}\right) = (-3.0, -3.0)\)

Q297. Find the point that divides the line segment joining \((-8, -2)\) and \((-1, 4)\) in the ratio 2:5.

A) -3.0, 2.29
B) -6.0, -0.29
C) -4.5, 1.0
D) -12.67, -6.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times-1+5\times-8}{2+5}, \frac{2\times4+5\times-2}{2+5}\right) = (-6.0, -0.29)\)

Q298. Find the point that divides the line segment joining \((-1, -2)\) and \((5, -2)\) in the ratio 3:2.

A) 2.6, -2.0
B) 2.0, -2.0
C) 17.0, -2.0
D) 1.4, -2.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times5+2\times-1}{3+2}, \frac{3\times-2+2\times-2}{3+2}\right) = (2.6, -2.0)\)

Q299. Find the point that divides the line segment joining \((4, -6)\) and \((-6, 2)\) in the ratio 4:3.

A) -36.0, 26.0
B) -0.29, -2.57
C) -1.0, -2.0
D) -1.71, -1.43

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times-6+3\times4}{4+3}, \frac{4\times2+3\times-6}{4+3}\right) = (-1.71, -1.43)\)

Q300. Find the point that divides the line segment joining \((1, -8)\) and \((0, -7)\) in the ratio 2:5.

A) 0.71, -7.71
B) 0.29, -7.29
C) 1.67, -8.67
D) 0.5, -7.5

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times0+5\times1}{2+5}, \frac{2\times-7+5\times-8}{2+5}\right) = (0.71, -7.71)\)

Q301. Find the point that divides the line segment joining \((7, -2)\) and \((6, -2)\) in the ratio 3:1.

A) 6.5, -2.0
B) 5.5, -2.0
C) 6.75, -2.0
D) 6.25, -2.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times6+1\times7}{3+1}, \frac{3\times-2+1\times-2}{3+1}\right) = (6.25, -2.0)\)

Q302. Find the point that divides the line segment joining \((3, -2)\) and \((4, 4)\) in the ratio 5:4.

A) 3.56, 1.33
B) 3.44, 0.67
C) 8.0, 28.0
D) 3.5, 1.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times4+4\times3}{5+4}, \frac{5\times4+4\times-2}{5+4}\right) = (3.56, 1.33)\)

Q303. Find the point that divides the line segment joining \((2, 3)\) and \((4, -1)\) in the ratio 2:4.

A) 2.67, 1.67
B) 3.0, 1.0
C) -0.0, 7.0
D) 3.33, 0.33

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times4+4\times2}{2+4}, \frac{2\times-1+4\times3}{2+4}\right) = (2.67, 1.67)\)

Q304. Find the point that divides the line segment joining \((3, -7)\) and \((-5, -1)\) in the ratio 2:3.

A) -1.8, -3.4
B) -0.2, -4.6
C) -1.0, -4.0
D) 19.0, -19.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times-5+3\times3}{2+3}, \frac{2\times-1+3\times-7}{2+3}\right) = (-0.2, -4.6)\)

Q305. Find the point that divides the line segment joining \((8, 8)\) and \((4, 5)\) in the ratio 4:4.

A) N/A (1)
B) 6.0, 6.5
C) -16, -12
D) N/A (2)

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times4+4\times8}{4+4}, \frac{4\times5+4\times8}{4+4}\right) = (6.0, 6.5)\)

Q306. Find the point that divides the line segment joining \((-1, 2)\) and \((-6, -5)\) in the ratio 5:4.

A) -3.78, -1.89
B) -26.0, -33.0
C) -3.22, -1.11
D) -3.5, -1.5

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times-6+4\times-1}{5+4}, \frac{5\times-5+4\times2}{5+4}\right) = (-3.78, -1.89)\)

Q307. Find the point that divides the line segment joining \((3, -2)\) and \((1, 4)\) in the ratio 5:3.

A) -2.0, 13.0
B) 1.75, 1.75
C) 2.0, 1.0
D) 2.25, 0.25

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times1+3\times3}{5+3}, \frac{5\times4+3\times-2}{5+3}\right) = (1.75, 1.75)\)

Q308. Find the point that divides the line segment joining \((-5, -7)\) and \((7, 7)\) in the ratio 1:5.

A) -8.0, -10.5
B) 1.0, 0.0
C) -3.0, -4.67
D) 5.0, 4.67

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{1\times7+5\times-5}{1+5}, \frac{1\times7+5\times-7}{1+5}\right) = (-3.0, -4.67)\)

Q309. Find the point that divides the line segment joining \((-3, -5)\) and \((7, 7)\) in the ratio 4:5.

A) 1.44, 0.33
B) -43.0, -53.0
C) 2.56, 1.67
D) 2.0, 1.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{4\times7+5\times-3}{4+5}, \frac{4\times7+5\times-5}{4+5}\right) = (1.44, 0.33)\)

Q310. Find the point that divides the line segment joining \((-1, -5)\) and \((-1, -4)\) in the ratio 3:3.

A) N/A (1)
B) N/A (2)
C) 0, 3
D) -1.0, -4.5

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times-1+3\times-1}{3+3}, \frac{3\times-4+3\times-5}{3+3}\right) = (-1.0, -4.5)\)

Q311. Find the point that divides the line segment joining \((-5, 6)\) and \((-6, 0)\) in the ratio 5:1.

A) -5.5, 3.0
B) -6.25, -1.5
C) -5.17, 5.0
D) -5.83, 1.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{5\times-6+1\times-5}{5+1}, \frac{5\times0+1\times6}{5+1}\right) = (-5.83, 1.0)\)

Q312. Find the point that divides the line segment joining \((-4, -1)\) and \((-2, -5)\) in the ratio 3:2.

A) 2.0, -13.0
B) -3.2, -2.6
C) -3.0, -3.0
D) -2.8, -3.4

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times-2+2\times-4}{3+2}, \frac{3\times-5+2\times-1}{3+2}\right) = (-2.8, -3.4)\)

Q313. Find the point that divides the line segment joining \((-4, -3)\) and \((4, -2)\) in the ratio 2:2.

A) 0.0, -2.5
B) N/A (1)
C) N/A (2)
D) 16, 2

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times4+2\times-4}{2+2}, \frac{2\times-2+2\times-3}{2+2}\right) = (0.0, -2.5)\)

Q314. Find the point that divides the line segment joining \((-3, -5)\) and \((6, 7)\) in the ratio 3:2.

A) 24.0, 31.0
B) 0.6, -0.2
C) 2.4, 2.2
D) 1.5, 1.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times6+2\times-3}{3+2}, \frac{3\times7+2\times-5}{3+2}\right) = (2.4, 2.2)\)

Q315. Find the point that divides the line segment joining \((8, -8)\) and \((-6, -7)\) in the ratio 3:3.

A) N/A (2)
B) N/A (1)
C) 1.0, -7.5
D) -42, 3

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{3\times-6+3\times8}{3+3}, \frac{3\times-7+3\times-8}{3+3}\right) = (1.0, -7.5)\)

Q316. Find the point that divides the line segment joining \((3, 2)\) and \((-5, -6)\) in the ratio 2:2.

A) N/A (1)
B) N/A (2)
C) -16, -16
D) -1.0, -2.0

Difficulty: Medium · Topic: Section formula (internal division)

Solution

Section formula: \(\left(\frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n}\right)\)

\(= \left(\frac{2\times-5+2\times3}{2+2}, \frac{2\times-6+2\times2}{2+2}\right) = (-1.0, -2.0)\)

Q317. Find the area of the triangle with vertices \((4,1)\), \((4,5)\), and \((3,4)\).

A) 2.0
B) 37.0
C) 19.5
D) 4

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|4(5-4)+4(4-1)+3(1-5)|\)

\(= 2.0\) sq. units

Q318. Find the area of the triangle with vertices \((4,7)\), \((1,3)\), and \((7,1)\).

A) 31.0
B) 30
C) 15.0
D) 47.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|4(3-1)+1(1-7)+7(7-3)|\)

\(= 15.0\) sq. units

Q319. Find the area of the triangle with vertices \((6,7)\), \((7,2)\), and \((3,6)\).

A) 83.0
B) 16
C) 37.5
D) 8.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|6(2-6)+7(6-7)+3(7-2)|\)

\(= 8.0\) sq. units

Q320. Find the area of the triangle with vertices \((5,8)\), \((8,5)\), and \((8,5)\).

A) 64.5
B) 1.0
C) 129.0
D) 0.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|5(5-5)+8(5-8)+8(8-5)|\)

\(= 0.0\) sq. units

Q321. Find the area of the triangle with vertices \((2,3)\), \((1,0)\), and \((0,5)\).

A) 8
B) 2.5
C) 4.0
D) 9.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(0-5)+1(5-3)+0(3-0)|\)

\(= 4.0\) sq. units

Q322. Find the area of the triangle with vertices \((3,6)\), \((4,1)\), and \((3,8)\).

A) 2
B) 26.5
C) 52.0
D) 1.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|3(1-8)+4(8-6)+3(6-1)|\)

\(= 1.0\) sq. units

Q323. Find the area of the triangle with vertices \((4,6)\), \((8,7)\), and \((1,8)\).

A) 11
B) 92.5
C) 49.0
D) 5.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|4(7-8)+8(8-6)+1(6-7)|\)

\(= 5.5\) sq. units

Q324. Find the area of the triangle with vertices \((1,5)\), \((5,0)\), and \((6,4)\).

A) 10.5
B) 39.5
C) 21
D) 25.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|1(0-4)+5(4-5)+6(5-0)|\)

\(= 10.5\) sq. units

Q325. Find the area of the triangle with vertices \((6,0)\), \((4,8)\), and \((7,8)\).

A) 12.0
B) 24
C) 92.0
D) 40.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|6(8-8)+4(8-0)+7(0-8)|\)

\(= 12.0\) sq. units

Q326. Find the area of the triangle with vertices \((8,4)\), \((0,2)\), and \((0,2)\).

A) 0.0
B) 1.0
C) 16.0
D) 8.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|8(2-2)+0(2-4)+0(4-2)|\)

\(= 0.0\) sq. units

Q327. Find the area of the triangle with vertices \((7,0)\), \((7,2)\), and \((1,5)\).

A) 12
B) 43.0
C) 6.0
D) 24.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|7(2-5)+7(5-0)+1(0-2)|\)

\(= 6.0\) sq. units

Q328. Find the area of the triangle with vertices \((7,0)\), \((1,3)\), and \((2,4)\).

A) 9
B) 12.5
C) 29.5
D) 4.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|7(3-4)+1(4-0)+2(0-3)|\)

\(= 4.5\) sq. units

Q329. Find the area of the triangle with vertices \((3,0)\), \((5,5)\), and \((8,0)\).

A) 25
B) 12.5
C) 27.5
D) 7.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|3(5-0)+5(0-0)+8(0-5)|\)

\(= 12.5\) sq. units

Q330. Find the area of the triangle with vertices \((5,3)\), \((2,3)\), and \((7,6)\).

A) 4.5
B) 52.5
C) 24.0
D) 9

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|5(3-6)+2(6-3)+7(3-3)|\)

\(= 4.5\) sq. units

Q331. Find the area of the triangle with vertices \((6,5)\), \((2,7)\), and \((5,5)\).

A) 1.0
B) 76.0
C) 2
D) 38.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|6(7-5)+2(5-5)+5(5-7)|\)

\(= 1.0\) sq. units

Q332. Find the area of the triangle with vertices \((2,6)\), \((3,8)\), and \((1,0)\).

A) 2.0
B) 4
C) 24.0
D) 11.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(8-0)+3(0-6)+1(6-8)|\)

\(= 2.0\) sq. units

Q333. Find the area of the triangle with vertices \((1,1)\), \((6,8)\), and \((7,5)\).

A) 56.0
B) 22.5
C) 11.0
D) 22

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|1(8-5)+6(5-1)+7(1-8)|\)

\(= 11.0\) sq. units

Q334. Find the area of the triangle with vertices \((0,7)\), \((5,1)\), and \((3,4)\).

A) 3
B) 39.5
C) 1.5
D) 20.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|0(1-4)+5(4-7)+3(7-1)|\)

\(= 1.5\) sq. units

Q335. Find the area of the triangle with vertices \((1,7)\), \((8,7)\), and \((2,4)\).

A) 26.5
B) 10.5
C) 21
D) 63.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|1(7-4)+8(4-7)+2(7-7)|\)

\(= 10.5\) sq. units

Q336. Find the area of the triangle with vertices \((4,6)\), \((7,7)\), and \((7,0)\).

A) 21
B) 35.0
C) 10.5
D) 80.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|4(7-0)+7(0-6)+7(6-7)|\)

\(= 10.5\) sq. units

Q337. Find the area of the triangle with vertices \((1,8)\), \((8,0)\), and \((6,7)\).

A) 52.0
B) 16.5
C) 87.5
D) 33

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|1(0-7)+8(7-8)+6(8-0)|\)

\(= 16.5\) sq. units

Q338. Find the area of the triangle with vertices \((5,8)\), \((1,8)\), and \((7,2)\).

A) 24
B) 12.0
C) 49.0
D) 86.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|5(8-2)+1(2-8)+7(8-8)|\)

\(= 12.0\) sq. units

Q339. Find the area of the triangle with vertices \((2,4)\), \((7,1)\), and \((6,0)\).

A) 13.0
B) 8
C) 4.0
D) 30.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(1-0)+7(0-4)+6(4-1)|\)

\(= 4.0\) sq. units

Q340. Find the area of the triangle with vertices \((1,4)\), \((1,1)\), and \((2,2)\).

A) 1.5
B) 9.5
C) 3
D) 5.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|1(1-2)+1(2-4)+2(4-1)|\)

\(= 1.5\) sq. units

Q341. Find the area of the triangle with vertices \((0,3)\), \((1,7)\), and \((1,5)\).

A) 2
B) 1.0
C) 9.0
D) 4.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|0(7-5)+1(5-3)+1(3-7)|\)

\(= 1.0\) sq. units

Q342. Find the area of the triangle with vertices \((8,4)\), \((1,3)\), and \((3,7)\).

A) 56.0
B) 21.5
C) 26
D) 13.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|8(3-7)+1(7-4)+3(4-3)|\)

\(= 13.0\) sq. units

Q343. Find the area of the triangle with vertices \((5,5)\), \((2,8)\), and \((3,8)\).

A) 35.5
B) 1.5
C) 3
D) 72.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|5(8-8)+2(8-5)+3(5-8)|\)

\(= 1.5\) sq. units

Q344. Find the area of the triangle with vertices \((3,8)\), \((7,7)\), and \((4,3)\).

A) 37.0
B) 19
C) 83.5
D) 9.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|3(7-3)+7(3-8)+4(8-7)|\)

\(= 9.5\) sq. units

Q345. Find the area of the triangle with vertices \((2,3)\), \((8,4)\), and \((6,5)\).

A) 4.0
B) 33.0
C) 62.0
D) 8

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(4-5)+8(5-3)+6(3-4)|\)

\(= 4.0\) sq. units

Q346. Find the area of the triangle with vertices \((1,3)\), \((6,6)\), and \((1,3)\).

A) 13.5
B) 0.0
C) 1.0
D) 27.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|1(6-3)+6(3-3)+1(3-6)|\)

\(= 0.0\) sq. units

Q347. Find the area of the triangle with vertices \((4,4)\), \((7,3)\), and \((6,0)\).

A) 10
B) 18.0
C) 5.0
D) 41.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|4(3-0)+7(0-4)+6(4-3)|\)

\(= 5.0\) sq. units

Q348. Find the area of the triangle with vertices \((8,8)\), \((6,8)\), and \((4,8)\).

A) 72.0
B) 144.0
C) 0.0
D) 1.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|8(8-8)+6(8-8)+4(8-8)|\)

\(= 0.0\) sq. units

Q349. Find the area of the triangle with vertices \((0,4)\), \((6,6)\), and \((4,7)\).

A) 5.0
B) 53.0
C) 29.0
D) 10

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|0(6-7)+6(7-4)+4(4-6)|\)

\(= 5.0\) sq. units

Q350. Find the area of the triangle with vertices \((4,0)\), \((3,5)\), and \((0,0)\).

A) 12.0
B) 10.0
C) 20
D) 11.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|4(5-0)+3(0-0)+0(0-5)|\)

\(= 10.0\) sq. units

Q351. Find the area of the triangle with vertices \((3,8)\), \((5,0)\), and \((4,3)\).

A) 1.0
B) 2
C) 23.5
D) 48.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|3(0-3)+5(3-8)+4(8-0)|\)

\(= 1.0\) sq. units

Q352. Find the area of the triangle with vertices \((3,1)\), \((8,6)\), and \((5,2)\).

A) 2.5
B) 41.5
C) 19.5
D) 5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|3(6-2)+8(2-1)+5(1-6)|\)

\(= 2.5\) sq. units

Q353. Find the area of the triangle with vertices \((2,1)\), \((5,4)\), and \((8,2)\).

A) 13.0
B) 7.5
C) 15
D) 33.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(4-2)+5(2-1)+8(1-4)|\)

\(= 7.5\) sq. units

Q354. Find the area of the triangle with vertices \((1,6)\), \((8,5)\), and \((1,8)\).

A) 14
B) 7.0
C) 37.5
D) 68.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|1(5-8)+8(8-6)+1(6-5)|\)

\(= 7.0\) sq. units

Q355. Find the area of the triangle with vertices \((3,1)\), \((4,1)\), and \((4,6)\).

A) 2.5
B) 28.5
C) 5
D) 15.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|3(1-6)+4(6-1)+4(1-1)|\)

\(= 2.5\) sq. units

Q356. Find the area of the triangle with vertices \((7,7)\), \((1,0)\), and \((7,8)\).

A) 3.0
B) 28.5
C) 60.0
D) 6

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|7(0-8)+1(8-7)+7(7-0)|\)

\(= 3.0\) sq. units

Q357. Find the area of the triangle with vertices \((2,0)\), \((0,6)\), and \((3,4)\).

A) 14
B) 19.0
C) 6.0
D) 7.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(6-4)+0(4-0)+3(0-6)|\)

\(= 7.0\) sq. units

Q358. Find the area of the triangle with vertices \((2,4)\), \((2,2)\), and \((0,4)\).

A) 6.0
B) 4
C) 14.0
D) 2.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(2-4)+2(4-4)+0(4-2)|\)

\(= 2.0\) sq. units

Q359. Find the area of the triangle with vertices \((4,4)\), \((1,3)\), and \((7,7)\).

A) 6
B) 50.0
C) 3.0
D) 23.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|4(3-7)+1(7-4)+7(4-3)|\)

\(= 3.0\) sq. units

Q360. Find the area of the triangle with vertices \((1,8)\), \((7,5)\), and \((6,5)\).

A) 1.5
B) 3
C) 89.5
D) 44.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|1(5-5)+7(5-8)+6(8-5)|\)

\(= 1.5\) sq. units

Q361. Find the area of the triangle with vertices \((7,6)\), \((5,7)\), and \((7,8)\).

A) 4
B) 2.0
C) 65.5
D) 133.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|7(7-8)+5(8-6)+7(6-7)|\)

\(= 2.0\) sq. units

Q362. Find the area of the triangle with vertices \((2,0)\), \((2,1)\), and \((0,8)\).

A) 17.0
B) 1.0
C) 2
D) 9.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(1-8)+2(8-0)+0(0-1)|\)

\(= 1.0\) sq. units

Q363. Find the area of the triangle with vertices \((7,7)\), \((3,6)\), and \((6,8)\).

A) 2.5
B) 5
C) 110.5
D) 54.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|7(6-8)+3(8-7)+6(7-6)|\)

\(= 2.5\) sq. units

Q364. Find the area of the triangle with vertices \((8,2)\), \((6,1)\), and \((3,0)\).

A) 1
B) 14.5
C) 7.0
D) 0.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|8(1-0)+6(0-2)+3(2-1)|\)

\(= 0.5\) sq. units

Q365. Find the area of the triangle with vertices \((3,8)\), \((2,3)\), and \((7,8)\).

A) 20
B) 10.0
C) 71.0
D) 40.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|3(3-8)+2(8-8)+7(8-3)|\)

\(= 10.0\) sq. units

Q366. Find the area of the triangle with vertices \((2,7)\), \((5,5)\), and \((5,1)\).

A) 25.0
B) 12
C) 56.0
D) 6.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(5-1)+5(1-7)+5(7-5)|\)

\(= 6.0\) sq. units

Q367. Find the area of the triangle with vertices \((7,4)\), \((5,5)\), and \((4,5)\).

A) 75.5
B) 1
C) 38.0
D) 0.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|7(5-5)+5(5-4)+4(4-5)|\)

\(= 0.5\) sq. units

Q368. Find the area of the triangle with vertices \((6,0)\), \((0,2)\), and \((1,2)\).

A) 2
B) 6.0
C) 13.0
D) 1.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|6(2-2)+0(2-0)+1(0-2)|\)

\(= 1.0\) sq. units

Q369. Find the area of the triangle with vertices \((2,6)\), \((2,8)\), and \((4,3)\).

A) 2.0
B) 48.0
C) 4
D) 23.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|2(8-3)+2(3-6)+4(6-8)|\)

\(= 2.0\) sq. units

Q370. Find the area of the triangle with vertices \((4,2)\), \((8,5)\), and \((1,3)\).

A) 39.5
B) 6.5
C) 23.0
D) 13

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|4(5-3)+8(3-2)+1(2-5)|\)

\(= 6.5\) sq. units

Q371. Find the area of the triangle with vertices \((7,7)\), \((2,1)\), and \((5,3)\).

A) 44.0
B) 8
C) 24.0
D) 4.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|7(1-3)+2(3-7)+5(7-1)|\)

\(= 4.0\) sq. units

Q372. Find the area of the triangle with vertices \((0,3)\), \((0,8)\), and \((4,5)\).

A) 22.0
B) 6.0
C) 20
D) 10.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|0(8-5)+0(5-3)+4(3-8)|\)

\(= 10.0\) sq. units

Q373. Find the area of the triangle with vertices \((7,8)\), \((2,4)\), and \((8,0)\).

A) 22.0
B) 44
C) 70.0
D) 46.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|7(4-0)+2(0-8)+8(8-4)|\)

\(= 22.0\) sq. units

Q374. Find the area of the triangle with vertices \((6,3)\), \((8,2)\), and \((7,3)\).

A) 0.5
B) 28.5
C) 1
D) 56.5

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|6(2-3)+8(3-3)+7(3-2)|\)

\(= 0.5\) sq. units

Q375. Find the area of the triangle with vertices \((1,8)\), \((1,2)\), and \((4,0)\).

A) 17.0
B) 18
C) 9.0
D) 25.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|1(2-0)+1(0-8)+4(8-2)|\)

\(= 9.0\) sq. units

Q376. Find the area of the triangle with vertices \((3,4)\), \((8,4)\), and \((2,4)\).

A) 26.0
B) 0.0
C) 52.0
D) 1.0

Difficulty: Medium · Topic: Area of triangle from coordinates

Solution

Area \(= \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(= \frac{1}{2}|3(4-4)+8(4-4)+2(4-4)|\)

\(= 0.0\) sq. units

Q377. If (1,2), (4,y), (x,6) and (3,5) are vertices of a parallelogram taken in order, find x and y.

Difficulty: Medium-Hard · Topic: Distance Formula

Solution

Diagonals of parallelogram bisect each other. Midpoint of (1,2)&(x,6) = midpoint of (4,y)&(3,5).

(1+x)/2 = 7/2 → x = 6. (2+6)/2 = (y+5)/2 → y = 3.

Q378. If the area of the triangle formed by (x,2x), (−2,6) and (3,1) is 5 sq units, find x.

Difficulty: Medium-Hard · Topic: Area of a Triangle

Solution

½|x(6−1)+(−2)(1−2x)+3(2x−6)| = 5.

½|5x−2+4x+6x−18| = 5 → ½|15x−20| = 5 → |15x−20| = 10.

15x−20 = 10 → x = 2. Or 15x−20 = −10 → x = 2/3.

Q379. Show that the points (a,a), (−a,−a) and (−a√3, a√3) form an equilateral triangle.

Difficulty: Medium-Hard · Topic: Distance Formula

Solution

AB = √[(−2a)²+(−2a)²] = √(8a²) = 2a√2.

BC = √[(−a√3+a)²+(a√3+a)²] = √[a²(√3−1)²+a²(√3+1)²] = a√[(4−2√3)+(4+2√3)] = a√8 = 2a√2.

AC = √[(−a√3−a)²+(a√3−a)²] = a√[(√3+1)²+(√3−1)²] = a√8 = 2a√2.

AB = BC = AC → equilateral.

Q380. Find the coordinates of the points of trisection of the line segment joining (4,−1) and (−2,−3).

Difficulty: Hard · Topic: Section Formula

Solution

P divides in 1:2: x = (−2+8)/3 = 2, y = (−3−2)/3 = −5/3. P(2,−5/3).

Q divides in 2:1: x = (−4+4)/3 = 0, y = (−6−1)/3 = −7/3. Q(0,−7/3).

Chapter 7: Coordinate Geometry

Important Formulas

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