Worksheet: Parallel and Perpendicular Lines

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In this worksheet, we will practice determining if two lines are parallel or perpendicular and using these geometrical relationships to solve problems.

Q1:

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

Q2:

A staight line 𝐿 has the equation 𝑦 = 3 𝑥 − 2 . Find the equation of the line perpendicular to 𝐿 that passes through the point ( 4 , 4 ) .

  • A 𝑦 = − 3 𝑥 + 1 6
  • B 𝑦 = 1 3 𝑥 + 8 3
  • C 𝑦 = 3 𝑥 − 8
  • D 𝑦 = − 1 3 𝑥 + 1 6 3
  • E 𝑦 = 2 𝑥 − 4

Q3:

If the line passing through points 𝐴 ( − 1 3 , 8 ) and 𝐵 ( 2 0 , 𝑦 ) is parallel to the line passing through points 𝐶 ( − 2 , 0 ) and 𝐷 ( 7 , 𝑦 ) , what is the value of 𝑦 ?

Q4:

Two lines 𝐴 and 𝐵 have slopes of 7 5 and − 5 7 respectively. Are the two lines perpendicular?

  • AYes
  • BNo

Q5:

Two lines 𝐴 and 𝐵 have slopes of − 3 5 and 5 3 respectively. Are the two lines parallel or perpendicular?

  • APerpendicular
  • BParallel

Q6:

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

  • A @ 𝑚 − @ 𝑚 ≠ 0
  • B @ 𝑚 @ 𝑚 = 0
  • C @ 𝑚 + @ 𝑚 = 0
  • D @ 𝑚 − @ 𝑚 = 0

Q7:

If ⃖ ⃗ 𝐴 𝐵 ⟂ ⃖ ⃗ 𝐶 𝐷 and the slope of ⃖ ⃗ 𝐴 𝐵 = 2 5 , find the slope of ⃖ ⃗ 𝐶 𝐷 .

  • A 2 5
  • B − 2 5
  • C 5 2
  • D − 5 2

Q8:

Suppose that 𝐿 is the line 𝑎 𝑥 − 2 𝑦 − 8 = 0 and 𝐿 the line − 3 𝑥 + 𝑦 + 2 = 0 . Find the value of 𝑎 so that 𝐿 ⟂ 𝐿 .

  • A 2 3
  • B6
  • C − 6
  • D − 2 3

Q9:

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 − 2 3
  • B − 8 7
  • C − 3 2
  • D − 7 8
  • E7

Q10:

If ⃖ ⃗ 𝐴 𝐵 ⫽ ⃖ ⃗ 𝐶 𝐷 and the slope of ⃖ ⃗ 𝐴 𝐵 = 7 , find the slope of ⃖ ⃗ 𝐶 𝐷 .

  • A − 1 7
  • B − 7
  • C 1 7
  • D 7

Q11:

If the two straight lines whose slopes are 3 2 and 𝑘 9 are perpendicular, what is the value of 𝑘 ?

Q12:

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

Q13:

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

  • A 𝑚 = − 𝑚
  • B 𝑚 = 𝑚
  • C 𝑚 𝑚 = 1
  • D 𝑚 𝑚 = − 1

Q14:

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

  • A − 3 8
  • B 3 8
  • C 8 3
  • D − 8 3

Q15:

Given that 𝐴 𝐵 𝐶 𝐷 is a trapezium, where 𝐴 𝐵 ⫽ 𝐶 𝐷 , 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 ( 6 , − 6 )
  • D ( 1 , − 1 )

Q16:

If the two straight lines 5 𝑥 + 𝑏 𝑦 + 1 = 0 and ⃑ 𝑟 = ( 7 , − 7 ) + 𝐾 ( 6 , 1 ) are parallel, find the value of 𝑏 .

Q17:

Let 𝐿 be the line parallel to the line 𝑦 + 1 𝑥 = − 7 2 and that has 𝑦 -intercept 7 . Give the equation of 𝐿 in the form 𝑦 = 𝑚 𝑥 + 𝑐 .

  • A 𝑦 = − 2 7 𝑥 + 7
  • B 𝑦 = 7 𝑥 − 7 2
  • C 𝑦 = 7 2 𝑥 + 7
  • D 𝑦 = − 7 2 𝑥 + 7

Q18:

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

  • A It is impossible to tell.
  • B Yes
  • C No

Q19:

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

Q20:

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

Q21:

The lines 𝑥 = 3 𝑡 − 2 , 𝑦 = 3 𝑡 + 2 , 𝑧 = 9 𝑡 − 2 and 𝑥 = 𝑎 𝑡 − 2 , 𝑦 = 𝑡 + 1 , 𝑧 = 𝑏 𝑡 − 2 are parallel. What is 𝑎 + 𝑏 ?

Q22:

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 ?

  • A 𝑥 = 4
  • B 𝑦 = − 1
  • C 𝑦 = 4
  • D 𝑥 = − 1
  • E 𝑦 = 0

Q23:

Which of the following lines is parallel to 𝑦 = 5 𝑥 + 8 ?

  • A 𝑦 = − 5 𝑥 + 8
  • B 5 𝑥 + 5 𝑦 = 1 0
  • C 𝑦 = − 1 5 𝑥 + 3
  • D 1 0 𝑥 − 2 𝑦 = 1 4
  • E 𝑦 = − 1 5 𝑥 + 8

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