Chapter 10: Straight Lines

NCERT Solutions for CBSE Class 10 Mathematics — 100 solved questions with detailed explanations.

100

Questions

Topics

Solved Questions

Q1. The slope of the line passing through (1,2) and (3,8) is:

Difficulty: Easy · Topic: Slope

Solution

m = (y₂-y₁)/(x₂-x₁) = (8-2)/(3-1) = 6/2 = 3.

Q2. Two lines are perpendicular if the product of their slopes is:

0
1
-1
Undefined

Difficulty: Easy · Topic: Perpendicularity

Solution

For perpendicular lines: m₁ × m₂ = -1.

Q3. Slope of line through (1,2) and (3,8) is:

Difficulty: Easy · Topic: Slope

Solution

m = (y₂-y₁)/(x₂-x₁) = (8-2)/(3-1) = 3.

Q4. Slope of line through (0,0) and (4,12) is:

Difficulty: Easy · Topic: Slope

Solution

m = (y₂-y₁)/(x₂-x₁) = (12-0)/(4-0) = 3.

Q5. Slope of line through (-1,3) and (5,9) is:

Difficulty: Easy · Topic: Slope

Solution

m = (y₂-y₁)/(x₂-x₁) = (9-3)/(5--1) = 1.

Q6. Slope of line through (2,5) and (6,13) is:

Difficulty: Easy · Topic: Slope

Solution

m = (y₂-y₁)/(x₂-x₁) = (13-5)/(6-2) = 2.

Q7. Slope of line through (1,1) and (4,7) is:

Difficulty: Easy · Topic: Slope

Solution

m = (y₂-y₁)/(x₂-x₁) = (7-1)/(4-1) = 2.

Q8. Slope of line through (3,-1) and (7,11) is:

Difficulty: Easy · Topic: Slope

Solution

m = (y₂-y₁)/(x₂-x₁) = (11--1)/(7-3) = 3.

Q9. Slope through (0,0) and (1,0):

Difficulty: Easy · Topic: Slope

Solution

m=(0-0)/(1-0)=0.

Q10. Slope through (0,0) and (1,1):

Difficulty: Easy · Topic: Slope

Solution

m=(1-0)/(1-0)=1.

Q11. Slope through (0,0) and (1,2):

Difficulty: Easy · Topic: Slope

Solution

m=(2-0)/(1-0)=2.

Q12. Slope through (0,0) and (1,3):

Difficulty: Easy · Topic: Slope

Solution

m=(3-0)/(1-0)=3.

Q13. Slope through (0,0) and (1,4):

Difficulty: Easy · Topic: Slope

Solution

m=(4-0)/(1-0)=4.

Q14. Slope through (0,0) and (1,5):

Difficulty: Easy · Topic: Slope

Solution

m=(5-0)/(1-0)=5.

Q15. Slope through (0,0) and (1,6):

Difficulty: Easy · Topic: Slope

Solution

m=(6-0)/(1-0)=6.

Q16. Slope through (0,0) and (1,7):

Difficulty: Easy · Topic: Slope

Solution

m=(7-0)/(1-0)=7.

Q17. Slope through (0,0) and (1,8):

Difficulty: Easy · Topic: Slope

Solution

m=(8-0)/(1-0)=8.

Q18. Slope through (0,0) and (1,9):

Difficulty: Easy · Topic: Slope

Solution

m=(9-0)/(1-0)=9.

Q19. Slope through (0,0) and (2,0):

Difficulty: Easy · Topic: Slope

Solution

m=(0-0)/(2-0)=0.

Q20. Slope through (0,0) and (2,1):

Difficulty: Easy · Topic: Slope

Solution

m=(1-0)/(2-0)=0.5.

Q21. Slope through (0,0) and (2,2):

Difficulty: Easy · Topic: Slope

Solution

m=(2-0)/(2-0)=1.

Q22. Slope through (0,0) and (2,3):

Difficulty: Easy · Topic: Slope

Solution

m=(3-0)/(2-0)=1.5.

Q23. Slope through (0,0) and (2,4):

Difficulty: Easy · Topic: Slope

Solution

m=(4-0)/(2-0)=2.

Q24. Slope through (0,0) and (2,5):

Difficulty: Easy · Topic: Slope

Solution

m=(5-0)/(2-0)=2.5.

Q25. Slope through (0,0) and (2,6):

Difficulty: Easy · Topic: Slope

Solution

m=(6-0)/(2-0)=3.

Q26. Slope through (0,0) and (2,7):

Difficulty: Easy · Topic: Slope

Solution

m=(7-0)/(2-0)=3.5.

Q27. Slope through (0,0) and (2,8):

Difficulty: Easy · Topic: Slope

Solution

m=(8-0)/(2-0)=4.

Q28. Slope through (0,0) and (2,9):

Difficulty: Easy · Topic: Slope

Solution

m=(9-0)/(2-0)=4.5.

Q29. Slope through (0,0) and (3,0):

Difficulty: Easy · Topic: Slope

Solution

m=(0-0)/(3-0)=0.

Q30. Slope through (0,0) and (3,1):

Difficulty: Easy · Topic: Slope

Solution

m=(1-0)/(3-0)=0.33.

Q31. Slope through (0,0) and (3,2):

Difficulty: Easy · Topic: Slope

Solution

m=(2-0)/(3-0)=0.67.

Q32. Slope through (0,0) and (3,3):

Difficulty: Easy · Topic: Slope

Solution

m=(3-0)/(3-0)=1.

Q33. Slope through (0,0) and (3,4):

Difficulty: Easy · Topic: Slope

Solution

m=(4-0)/(3-0)=1.33.

Q34. Slope through (0,0) and (3,5):

Difficulty: Easy · Topic: Slope

Solution

m=(5-0)/(3-0)=1.67.

Q35. Slope through (0,0) and (3,6):

Difficulty: Easy · Topic: Slope

Solution

m=(6-0)/(3-0)=2.

Q36. Slope through (0,0) and (3,7):

Difficulty: Easy · Topic: Slope

Solution

m=(7-0)/(3-0)=2.33.

Q37. Slope through (0,0) and (3,8):

Difficulty: Easy · Topic: Slope

Solution

m=(8-0)/(3-0)=2.67.

Q38. Slope through (0,0) and (3,9):

Difficulty: Easy · Topic: Slope

Solution

m=(9-0)/(3-0)=3.

Q39. Slope through (0,0) and (4,0):

Difficulty: Easy · Topic: Slope

Solution

m=(0-0)/(4-0)=0.

Q40. Slope through (0,0) and (4,1):

Difficulty: Easy · Topic: Slope

Solution

m=(1-0)/(4-0)=0.25.

Q41. Slope through (0,0) and (4,2):

Difficulty: Easy · Topic: Slope

Solution

m=(2-0)/(4-0)=0.5.

Q42. Slope through (0,0) and (4,3):

Difficulty: Easy · Topic: Slope

Solution

m=(3-0)/(4-0)=0.75.

Q43. Slope through (0,0) and (4,4):

Difficulty: Easy · Topic: Slope

Solution

m=(4-0)/(4-0)=1.

Q44. Slope through (0,0) and (4,5):

Difficulty: Easy · Topic: Slope

Solution

m=(5-0)/(4-0)=1.25.

Q45. Slope through (0,0) and (4,6):

Difficulty: Easy · Topic: Slope

Solution

m=(6-0)/(4-0)=1.5.

Q46. Slope through (0,0) and (4,7):

Difficulty: Easy · Topic: Slope

Solution

m=(7-0)/(4-0)=1.75.

Q47. Slope through (0,0) and (4,8):

Difficulty: Easy · Topic: Slope

Solution

m=(8-0)/(4-0)=2.

Q48. Slope through (0,0) and (4,9):

Difficulty: Easy · Topic: Slope

Solution

m=(9-0)/(4-0)=2.25.

Q49. Slope through (0,0) and (5,0):

Difficulty: Easy · Topic: Slope

Solution

m=(0-0)/(5-0)=0.

Q50. Slope through (0,0) and (5,1):

Difficulty: Easy · Topic: Slope

Solution

m=(1-0)/(5-0)=0.2.

Q51. Slope through (0,0) and (5,2):

Difficulty: Easy · Topic: Slope

Solution

m=(2-0)/(5-0)=0.4.

Q52. Slope through (0,0) and (5,3):

Difficulty: Easy · Topic: Slope

Solution

m=(3-0)/(5-0)=0.6.

Q53. Slope through (0,0) and (5,4):

Difficulty: Easy · Topic: Slope

Solution

m=(4-0)/(5-0)=0.8.

Q54. Slope through (0,0) and (5,5):

Difficulty: Easy · Topic: Slope

Solution

m=(5-0)/(5-0)=1.

Q55. Slope through (0,0) and (5,6):

Difficulty: Easy · Topic: Slope

Solution

m=(6-0)/(5-0)=1.2.

Q56. Slope through (0,0) and (5,7):

Difficulty: Easy · Topic: Slope

Solution

m=(7-0)/(5-0)=1.4.

Q57. Slope through (0,0) and (5,8):

Difficulty: Easy · Topic: Slope

Solution

m=(8-0)/(5-0)=1.6.

Q58. Slope through (0,0) and (5,9):

Difficulty: Easy · Topic: Slope

Solution

m=(9-0)/(5-0)=1.8.

Q59. Slope through (0,0) and (6,0):

Difficulty: Easy · Topic: Slope

Solution

m=(0-0)/(6-0)=0.

Q60. Slope through (0,0) and (6,1):

Difficulty: Easy · Topic: Slope

Solution

m=(1-0)/(6-0)=0.17.

Q61. Slope through (0,0) and (6,2):

Difficulty: Easy · Topic: Slope

Solution

m=(2-0)/(6-0)=0.33.

Q62. Slope through (0,0) and (6,3):

Difficulty: Easy · Topic: Slope

Solution

m=(3-0)/(6-0)=0.5.

Q63. Slope through (0,0) and (6,4):

Difficulty: Easy · Topic: Slope

Solution

m=(4-0)/(6-0)=0.67.

Q64. Slope through (0,0) and (6,5):

Difficulty: Easy · Topic: Slope

Solution

m=(5-0)/(6-0)=0.83.

Q65. Slope through (0,0) and (6,6):

Difficulty: Easy · Topic: Slope

Solution

m=(6-0)/(6-0)=1.

Q66. Slope through (0,0) and (6,7):

Difficulty: Easy · Topic: Slope

Solution

m=(7-0)/(6-0)=1.17.

Q67. Slope through (0,0) and (6,8):

Difficulty: Easy · Topic: Slope

Solution

m=(8-0)/(6-0)=1.33.

Q68. Slope through (0,0) and (6,9):

Difficulty: Easy · Topic: Slope

Solution

m=(9-0)/(6-0)=1.5.

Q69. Slope through (0,0) and (7,0):

Difficulty: Easy · Topic: Slope

Solution

m=(0-0)/(7-0)=0.

Q70. Slope through (0,0) and (7,1):

Difficulty: Easy · Topic: Slope

Solution

m=(1-0)/(7-0)=0.14.

Q71. Slope through (0,0) and (7,2):

Difficulty: Easy · Topic: Slope

Solution

m=(2-0)/(7-0)=0.29.

Q72. Slope through (0,0) and (7,3):

Difficulty: Easy · Topic: Slope

Solution

m=(3-0)/(7-0)=0.43.

Q73. Slope through (0,0) and (7,4):

Difficulty: Easy · Topic: Slope

Solution

m=(4-0)/(7-0)=0.57.

Q74. Slope through (0,0) and (7,5):

Difficulty: Easy · Topic: Slope

Solution

m=(5-0)/(7-0)=0.71.

Q75. Slope through (0,0) and (7,6):

Difficulty: Easy · Topic: Slope

Solution

m=(6-0)/(7-0)=0.86.

Q76. Slope through (0,0) and (7,7):

Difficulty: Easy · Topic: Slope

Solution

m=(7-0)/(7-0)=1.

Q77. Slope through (0,0) and (7,8):

Difficulty: Easy · Topic: Slope

Solution

m=(8-0)/(7-0)=1.14.

Q78. Slope through (0,0) and (7,9):

Difficulty: Easy · Topic: Slope

Solution

m=(9-0)/(7-0)=1.29.

Q79. Slope through (0,0) and (8,0):

Difficulty: Easy · Topic: Slope

Solution

m=(0-0)/(8-0)=0.

Q80. Slope through (0,0) and (8,1):

Difficulty: Easy · Topic: Slope

Solution

m=(1-0)/(8-0)=0.12.

Q81. Slope through (0,0) and (8,2):

Difficulty: Easy · Topic: Slope

Solution

m=(2-0)/(8-0)=0.25.

Q82. Slope through (0,0) and (8,3):

Difficulty: Easy · Topic: Slope

Solution

m=(3-0)/(8-0)=0.38.

Q83. Slope through (0,0) and (8,4):

Difficulty: Easy · Topic: Slope

Solution

m=(4-0)/(8-0)=0.5.

Q84. Slope through (0,0) and (8,5):

Difficulty: Easy · Topic: Slope

Solution

m=(5-0)/(8-0)=0.62.

Q85. Slope through (0,0) and (8,6):

Difficulty: Easy · Topic: Slope

Solution

m=(6-0)/(8-0)=0.75.

Q86. Slope through (0,0) and (8,7):

Difficulty: Easy · Topic: Slope

Solution

m=(7-0)/(8-0)=0.88.

Q87. Slope through (0,0) and (8,8):

Difficulty: Easy · Topic: Slope

Solution

m=(8-0)/(8-0)=1.

Q88. Slope through (0,0) and (8,9):

Difficulty: Easy · Topic: Slope

Solution

m=(9-0)/(8-0)=1.12.

Q89. Slope through (0,0) and (9,0):

Difficulty: Easy · Topic: Slope

Solution

m=(0-0)/(9-0)=0.

Q90. Slope through (0,0) and (9,1):

Difficulty: Easy · Topic: Slope

Solution

m=(1-0)/(9-0)=0.11.

Q91. Slope through (0,0) and (9,2):

Difficulty: Easy · Topic: Slope

Solution

m=(2-0)/(9-0)=0.22.

Q92. Slope through (0,0) and (9,3):

Difficulty: Easy · Topic: Slope

Solution

m=(3-0)/(9-0)=0.33.

Q93. Slope through (0,0) and (9,4):

Difficulty: Easy · Topic: Slope

Solution

m=(4-0)/(9-0)=0.44.

Q94. Slope through (0,0) and (9,5):

Difficulty: Easy · Topic: Slope

Solution

m=(5-0)/(9-0)=0.56.

Q95. The distance of the point (3,4) from the line 3x + 4y - 5 = 0 is:

Difficulty: Easy-Medium · Topic: Distance

Solution

d = |3(3)+4(4)-5|/√(9+16) = |9+16-5|/5 = 20/5 = 4.

Q96. Distance of (1,2) from line 3x+4y+-5=0 is:

Difficulty: Easy-Medium · Topic: Distance

Solution

d = |3(1)+4(2)+(-5)|/√(3²+4²) = 1.2.

Q97. Distance of (2,3) from line 1x+1y+-3=0 is:

Difficulty: Easy-Medium · Topic: Distance

Solution

d = |1(2)+1(3)+(-3)|/√(1²+1²) = 1.41.

Q98. Distance of (1,1) from line 2x+-1y+4=0 is:

Difficulty: Easy-Medium · Topic: Distance

Solution

d = |2(1)+-1(1)+(4)|/√(2²+-1²) = 2.24.

Q99. Distance of (3,4) from line 1x+2y+-6=0 is:

Difficulty: Easy-Medium · Topic: Distance

Solution

d = |1(3)+2(4)+(-6)|/√(1²+2²) = 2.24.

Q100. Distance of (2,1) from line 3x+-4y+7=0 is:

Difficulty: Easy-Medium · Topic: Distance

Solution

d = |3(2)+-4(1)+(7)|/√(3²+-4²) = 1.8.

Other Chapters in Mathematics

Ch 1: Sets Ch 2: Relations & Functions Ch 3: Trigonometric Functions Ch 4: Principle of Mathematical Induction Ch 5: Complex Numbers Ch 6: Linear Inequalities Ch 7: Permutations & Combinations Ch 8: Binomial Theorem Ch 9: Sequences & Series Ch 11: Conic Sections Ch 12: Intro to 3D Geometry Ch 13: Limits & Derivatives Ch 14: Mathematical Reasoning Ch 15: Statistics Ch 16: Probability

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