51. In triangle ABC, mAB = 1 and mAC = 0. Then the angle between AB and AC is:
- 90^circ
- 60^circ
- 0^circ
- 45^circ
Answer: D) 45^circ
Explanation: tantheta = 0 - 11 + 0 = 1. SLO M-09-B-12 · Knowledge
MCQs / Mathematics / Angle Between Lines
Angle Between Lines MCQs — Mathematics (page 3)
63 multiple-choice questions on Angle Between Lines from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.
52. For the acute angle theta between lines with slopes 1 and 2, tantheta =
- 1
- 13
- 43
- 3
Answer: B) 13
Explanation: tantheta = m2 - m11 + m1 m2 = 13 = 13. SLO M-09-B-10 · Knowledge
53. Find the line through the intersection of x - y - 5 = 0 and 3x - y - 11 = 0 that also passes through (5, 2).
- 2x + y - 8 = 0
- 2x - y - 8 = 0
- 2x - y + 8 = 0
- x - 2y + 8 = 0
Answer: B) 2x - y - 8 = 0
Explanation: The lines meet at (3, -2). The line through (3, -2) and (5, 2) is 2x - y - 8 = 0 (you can also use L1 + kL2 = 0 and find k from the point). SLO M-09-B-11 · Understanding
54. The angle between lines with slopes 2 and - 12 is:
- 90^circ
- 0^circ
- 45^circ
- 60^circ
Answer: A) 90^circ
Explanation: m1 m2 = -1 = -1, so the lines are perpendicular. SLO M-09-B-10 · Knowledge
55. Find the point of intersection of x - y + 4 = 0 and x + 3y - 8 = 0.
- (3, -1)
- (1, 3)
- (-1, -3)
- (-1, 3)
Answer: D) (-1, 3)
Explanation: Solve the two equations together: x = -1, y = 3. Check: both equations are satisfied by (-1, 3). SLO M-09-B-11 · Understanding
56. Two lines 2x + 3y = 5 and 4x + 6y = 7:
- do not intersect (they are parallel)
- meet at the origin
- meet at (1, 1)
- are the same line
Answer: A) do not intersect (they are parallel)
Explanation: Both have slope - 23 but different constants, so they never meet. SLO M-09-B-11 · Understanding
57. The line through the intersection of x + y + 3 = 0 and 2x - 3y + 1 = 0, parallel to the y-axis, is:
- x = 2
- x = -1
- y = -1
- x = -2
Answer: D) x = -2
Explanation: The lines meet at (-2, -1); a vertical line through it is x = -2. SLO M-09-B-11 · Understanding
58. Find the point of intersection of 2x + y - 5 = 0 and x + 3y - 5 = 0.
- (2, 1)
- (1, 2)
- (2, -1)
- (-2, 1)
Answer: A) (2, 1)
Explanation: Solve the two equations together: x = 2, y = 1. Check: both equations are satisfied by (2, 1). SLO M-09-B-11 · Understanding
59. For the acute angle theta between lines with slopes 2 and 3, tantheta =
- 17
- 1
- 7
- 15
Answer: A) 17
Explanation: tantheta = m2 - m11 + m1 m2 = 17 = 17. SLO M-09-B-10 · Knowledge
60. The formula for the angle theta between two lines with slopes m1 and m2 is:
- tantheta = m2 + m11 - m1 m2
- tantheta = m1 m2
- tantheta = m2 - m11 + m1 m2
- tantheta = 1 + m1 m2m2 - m1
Answer: C) tantheta = m2 - m11 + m1 m2
Explanation: If tanalpha1 = m1 and tanalpha2 = m2, then theta = alpha2 - alpha1 and tan(alpha2 - alpha1) = m2 - m11 + m1 m2. SLO M-09-B-10 · Knowledge
61. The sides of a triangle have slopes 0, 1 and -1. Its angles are:
- 45^circ, 67.5^circ, 67.5^circ
- 60^circ, 60^circ, 60^circ
- 45^circ, 45^circ, 90^circ
- 30^circ, 60^circ, 90^circ
Answer: C) 45^circ, 45^circ, 90^circ
Explanation: Slopes 1 and -1 are perpendicular (1 -1 = -1); each makes 45^circ with the horizontal side. SLO M-09-B-12 · Knowledge
62. The sum of the three angles found from the slopes of a triangle's sides must be:
- 270^circ
- 180^circ
- 360^circ
- 90^circ
Answer: B) 180^circ
Explanation: This is a good check on your working. SLO M-09-B-12 · Knowledge
63. The angle between lines with slopes 14 and -4 is:
- 90^circ
- 45^circ
- 60^circ
- 0^circ
Answer: A) 90^circ
Explanation: m1 m2 = -1 = -1, so the lines are perpendicular. SLO M-09-B-10 · Knowledge
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Practise Angle Between Lines MCQs