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Worksheet: Parallel and Perpendicular Lines

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 π‘₯ βˆ’ 2 . Find the equation of the line perpendicular to 𝐿 that passes through the point ( 4 , 4 ) .

  • A 𝑦 = βˆ’ 3 π‘₯ + 1 6
  • B 𝑦 = 1 3 π‘₯ + 8 3
  • C 𝑦 = 3 π‘₯ βˆ’ 8
  • D 𝑦 = βˆ’ 1 3 π‘₯ + 1 6 3
  • E 𝑦 = 2 π‘₯ βˆ’ 4

Q3:

The lines π‘₯ = 3 𝑑 βˆ’ 2 1 , 𝑦 = 3 𝑑 + 2 1 , 𝑧 = 9 𝑑 βˆ’ 2 1 and π‘₯ = π‘Ž 𝑑 βˆ’ 2 2 , 𝑦 = 𝑑 + 1 2 , 𝑧 = 𝑏 𝑑 βˆ’ 2 2 are parallel. What is π‘Ž + 𝑏 ?

Q4:

Which of the following relates the slopes @ π‘š 1 and @ π‘š 2 of two parallel lines?

  • A @ π‘š βˆ’ @ π‘š β‰  0 1 2
  • B @ π‘š @ π‘š = 0 1 2
  • C @ π‘š + @ π‘š = 0 1 2
  • D @ π‘š βˆ’ @ π‘š = 0 1 2

Q5:

If and the gradient of , find the gradient of .

  • A
  • B
  • C
  • D

Q6:

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

Q7:

Two lines 𝐴 and 𝐡 have slopes of βˆ’ 3 5 and 5 3 respectively. Are the two lines parallel or perpendicular?

  • APerpendicular
  • BParallel

Q8:

The slope of the straight line that is parallel to the π‘₯ -axis is .

Q9:

The coordinates of points 𝐴 , 𝐡 , 𝐢 , and 𝐷 are ( 3 , 2 ) , ( βˆ’ 1 , 7 ) , ( 3 , 1 ) , and (9, 2) respectively. Are the line segments 𝐴 𝐡 and 𝐢 𝐷 perpendicular?

  • A It is impossible to tell.
  • B yes
  • C no

Q10:

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

  • A π‘₯ = 4
  • B 𝑦 = βˆ’ 1
  • C 𝑦 = 4
  • D π‘₯ = βˆ’ 1
  • E 𝑦 = 0

Q11:

Suppose that 𝐿 1 is the line π‘Ž π‘₯ βˆ’ 2 𝑦 βˆ’ 8 = 0 and 𝐿 2 the line βˆ’ 3 π‘₯ + 𝑦 + 2 = 0 . Find the value of π‘Ž so that 𝐿 βŸ‚ 𝐿 1 2 .

  • A 2 3
  • B6
  • C βˆ’ 6
  • D βˆ’ 2 3

Q12:

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

  • A βˆ’ 2 3
  • B βˆ’ 8 7
  • C βˆ’ 3 2
  • D βˆ’ 7 8
  • E7

Q13:

If and the gradient of , find the gradient of .

  • A
  • B
  • C
  • D 7

Q14:

If the two straight lines whose gradients are and are perpendicular, what is the value of ?

  • A2
  • B
  • C6
  • D
  • E3

Q15:

Suppose that the points , and are such that . What is the value of ?

Q16:

Which of the following relates the slopes π‘š 1 and π‘š 2 of two perpendicular lines?

  • A π‘š = βˆ’ π‘š 1 2
  • B π‘š = π‘š 1 2
  • C π‘š π‘š = 1 1 2
  • D π‘š π‘š = βˆ’ 1 1 2

Q17:

Let be the line on points and . What is the gradient of the perpendicular to that passes through the origin ?

  • A
  • B
  • C
  • D

Q18:

Given that is a trapezoid, where , and the coordinates of points , , , and are , , , and , respectively, find the coordinates of point .

  • A
  • B
  • C
  • D

Q19:

If the two straight lines and are parallel, find the value of .

Q20:

Two lines 𝐴 and 𝐡 have slopes of 7 5 and βˆ’ 5 7 respectively. Are the two lines perpendicular?

  • AYes
  • BNo

Q21:

Let 𝐿 be the line parallel to the line 𝑦 + 1 π‘₯ = βˆ’ 7 2 and that has 𝑦 -intercept 7 . Give the equation of 𝐿 in the form 𝑦 = π‘š π‘₯ + 𝑐 .

  • A 𝑦 = βˆ’ 2 7 π‘₯ + 7
  • B 𝑦 = 7 π‘₯ βˆ’ 7 2
  • C 𝑦 = 7 2 π‘₯ + 7
  • D 𝑦 = βˆ’ 7 2 π‘₯ + 7

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