Lesson Worksheet: Slopes of Parallel and Perpendicular Lines Mathematics

In this worksheet, we will practice using the concept of slopes to determine whether two lines are parallel or perpendicular and using these geometric relationships to solve problems.

Q1:

Two lines are perpendicular. What will the product of their slopes be?

Q2:

If the line passing through points 𝐴(−13,8) and 𝐵(20,𝑦) is parallel to the line passing through points 𝐶(−2,0) and 𝐷(7,𝑦), what is the value of 𝑦?

Q3:

Two lines 𝐴 and 𝐵 have slopes of 75 and −57 respectively. Are the two lines perpendicular?

  • AYes
  • BNo

Q4:

Two lines 𝐴 and 𝐵 have slopes of −35 and 53 respectively. Are the two lines parallel or perpendicular?

  • AParallel
  • BPerpendicular

Q5:

Which of the following relates the slopes 𝑚 and 𝑚 of two parallel lines?

  • A𝑚−𝑚≠0
  • B𝑚𝑚=0
  • C𝑚−𝑚=0
  • D𝑚+𝑚=0

Q6:

If ⃖⃗𝐴𝐵⟂⃖⃗𝐶𝐷 and the slope of ⃖⃗𝐴𝐵=25, find the slope of ⃖⃗𝐶𝐷.

  • A−52
  • B25
  • C−25
  • D52

Q7:

Find the gradient of the straight line which is parallel to the straight line passing through the points 𝐴(−7,8) and 𝐵(1,1).

  • A−32
  • B−87
  • C−23
  • D−78
  • E7

Q8:

If ⃖⃗𝐴𝐵∥⃖⃗𝐶𝐷 and the slope of ⃖⃗𝐴𝐵=7, find the slope of ⃖⃗𝐶𝐷.

  • A−7
  • B−17
  • C17
  • D7

Q9:

If the two straight lines whose slopes are 32 and 𝑘9 are perpendicular, what is the value of 𝑘?

Q10:

Suppose that the points 𝐴(−5,3),𝐵(−8,−6),𝐶(7,5), and 𝐷(𝑥,8) are such that ⃖⃗𝐴𝐵∥⃖⃗𝐶𝐷. What is the value of 𝑥?

Q11:

Which of the following relates the slopes 𝑚 and 𝑚 of two perpendicular lines?

  • A𝑚𝑚=−1
  • B𝑚𝑚=1
  • C𝑚=−𝑚
  • D𝑚=𝑚

Q12:

Let 𝐿 be the line on points (−10,−1) and (6,5). What is the slope of the perpendicular to 𝐿 that passes through the origin (0,0)?

  • A38
  • B83
  • C−83
  • D−38

Q13:

Given that 𝐴𝐵𝐶𝐷 is a trapezoid, where 𝐴𝐵∥𝐶𝐷, and the coordinates of points 𝐴, 𝐵, 𝐶, and 𝐷 are (−5,−5), (−1,−1), (𝑥,−𝑥), and (−7,−9), respectively, find the coordinates of point 𝐶.

  • A(6,−6)
  • B(1,−1)
  • C(−1,1)
  • D(−6,6)

Q14:

The coordinates of points 𝐴, 𝐵, 𝐶, and 𝐷 are (3,2), (−1,7), (3,1), and (9,2) respectively. Are the line segments 𝐴𝐵 and 𝐶𝐷 perpendicular?

  • AYes
  • BIt is impossible to tell.
  • CNo

Q15:

Complete the following definition. Two line segments are said to be perpendicular if the product of their slopes is .

Q16:

The slope of the straight line that is parallel to the 𝑥-axis is .

Q17:

Lines 𝐴 and 𝐵 are perpendicular to each other and meet at (−1,4). If the slope of 𝐴 is 0, what is the equation of line 𝐵?

  • A𝑥=4
  • B𝑦=4
  • C𝑥=−1
  • D𝑦=0
  • E𝑦=−1

Q18:

What is the value of 𝑏, if lines −2𝑥+𝑏𝑦+6=0 and −𝑥−4𝑦−3=0 are parallel?

  • A−8
  • B−4
  • C−2
  • D12

Q19:

Two lines have slopes of 65 and 1210, and cut the 𝑦-axis at different points. Are the two lines parallel?

  • ANo
  • BYes

Q20:

The line 𝐿 passes through the points (3,3) and (−1,0), and the line 𝐿 passes through the points (−3,2) and (0,−2). Are the two lines perpendicular?

  • ANo
  • BYes

Q21:

Let 𝐿 be the line through the points (−7,−7) and (−9,6) and 𝑀 the line through (1,1) and (14,3). Which of the following is true about the lines 𝐿 and 𝑀?

  • AThey are intersecting but not perpendicular .
  • BThey are parallel.
  • CThey are perpendicular.

Q22:

If the line that passes through the points 𝐴(6,0) and 𝐵(4,−6) is perpendicular to the line passing through the points 𝐶(−9,19) and 𝐷(𝑥,15), what is the value of 𝑥?

Q23:

The line on the points (10,𝑘+2) and 𝐵(7,10) is parallel to one that makes an angle of 100∘ with the positive 𝑥-axis. Determine 𝑘 to the nearest integer.

Q24:

Two lines 𝐴 and 𝐵 have slopes of 89 and −1816 respectively. Are the two lines perpendicular?

  • AYes
  • BNo

Q25:

The line through points (−7,0) and (−2,𝑝) is perpendicular to the line −8𝑝−4𝑥+9=0. Find 𝑝.

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