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Lesson: Parallel and Perpendicular Lines

In this lesson, we will learn how to determine if two lines are parallel or perpendicular and use these geometrical relationships to solve problems.

Video

17:54

Sample Question Videos

01:03
04:32
04:21

Worksheet • 21 Questions • 4 Videos

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

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 = 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 β‰  0 1 2

Q5:

If βƒ–     βƒ— 𝐴 𝐡 βŸ‚ βƒ–     βƒ— 𝐢 𝐷 and the slope of βƒ–     βƒ— 𝐴 𝐡 = 2 5 , find the slope of βƒ–     βƒ— 𝐢 𝐷 .

  • A βˆ’ 5 2
  • B βˆ’ 2 5
  • C 5 2
  • D 2 5

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?

  • AParallel
  • BPerpendicular

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

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

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 βˆ’ 2 3
  • B6
  • C βˆ’ 6
  • D 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’ 7 8
  • B7
  • C βˆ’ 8 7
  • D βˆ’ 3 2
  • E βˆ’ 2 3

Q13:

If βƒ–     βƒ— 𝐴 𝐡 βˆ₯ βƒ–     βƒ— 𝐢 𝐷 and the slope of βƒ–     βƒ— 𝐴 𝐡 = 7 , find the slope of βƒ–     βƒ— 𝐢 𝐷 .

  • A 7
  • B βˆ’ 7
  • C 1 7
  • D βˆ’ 1 7

Q14:

If the two straight lines whose slopes are 3 2 and π‘˜ 9 are perpendicular, what is the value of π‘˜ ?

Q15:

Suppose that the points 𝐴 ( βˆ’ 5 , 3 ) , 𝐡 ( βˆ’ 8 , βˆ’ 6 ) , 𝐢 ( 7 , 5 ) , and 𝐷 ( π‘₯ , 8 ) are such that βƒ–     βƒ— 𝐴 𝐡 βˆ₯ βƒ–     βƒ— 𝐢 𝐷 . What is the value of π‘₯ ?

Q16:

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

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

Q17:

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

  • A βˆ’ 8 3
  • B 3 8
  • C 8 3
  • D βˆ’ 3 8

Q18:

Given that 𝐴 𝐡 𝐢 𝐷 is a trapezium, where 𝐴 𝐡 βˆ₯ 𝐢 𝐷 , and the coordinates of points 𝐴 , 𝐡 , 𝐢 , and 𝐷 are ( βˆ’ 5 , βˆ’ 5 ) , ( βˆ’ 1 , βˆ’ 1 ) , ( π‘₯ , βˆ’ π‘₯ ) , and ( βˆ’ 7 , βˆ’ 9 ) , respectively, find the coordinates of point 𝐢 .

  • A ( 1 , βˆ’ 1 )
  • B ( βˆ’ 1 , 1 )
  • C ( 6 , βˆ’ 6 )
  • D ( βˆ’ 6 , 6 )

Q19:

If the two straight lines 5 π‘₯ + 𝑏 𝑦 + 1 = 0 and ⃑ π‘Ÿ = ( 7 , βˆ’ 7 ) + 𝐾 ( 6 , 1 ) are parallel, find the value of 𝑏 .

Q20:

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

  • ANo
  • BYes

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