Worksheet: Slopes of Parallel and Perpendicular Lines

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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(βˆ’13,8) and 𝐡(20,𝑦) is parallel to the line passing through points 𝐢(βˆ’2,0) and 𝐷(7,𝑦), what is the value of 𝑦?

Q3:

Two lines 𝐴 and 𝐡 have slopes of 75 and βˆ’57 respectively. Are the two lines perpendicular?

  • AYes
  • BNo

Q4:

Two lines 𝐴 and 𝐡 have slopes of βˆ’35 and 53 respectively. Are the two lines parallel or perpendicular?

  • AParallel
  • BPerpendicular

Q5:

Which of the following relates the slopes π‘šοŠ§ and π‘šοŠ¨ of two parallel lines?

  • Aπ‘šβˆ’π‘šβ‰ 0
  • Bπ‘šπ‘š=0
  • Cπ‘šβˆ’π‘š=0
  • Dπ‘š+π‘š=0

Q6:

If βƒ–οƒ©οƒ©οƒ©οƒ©βƒ—π΄π΅βŸ‚βƒ–οƒ©οƒ©οƒ©οƒ©βƒ—πΆπ· and the slope of ⃖⃗𝐴𝐡=25, find the slope of ⃖⃗𝐢𝐷.

  • Aβˆ’52
  • B25
  • Cβˆ’25
  • D52

Q7:

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).

  • Aβˆ’32
  • Bβˆ’87
  • Cβˆ’23
  • Dβˆ’78
  • E7

Q8:

If ⃖⃗𝐴𝐡βˆ₯⃖⃗𝐢𝐷 and the slope of ⃖⃗𝐴𝐡=7, find the slope of ⃖⃗𝐢𝐷.

  • Aβˆ’7
  • Bβˆ’17
  • C17
  • D7

Q9:

If the two straight lines whose slopes are 32 and π‘˜9 are perpendicular, what is the value of π‘˜?

Q10:

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

Q11:

Which of the following relates the slopes π‘šοŠ§ and π‘šοŠ¨ of two perpendicular lines?

  • Aπ‘šπ‘š=βˆ’1
  • Bπ‘šπ‘š=1
  • Cπ‘š=βˆ’π‘šοŠ§οŠ¨
  • Dπ‘š=π‘šοŠ§οŠ¨

Q12:

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

  • A38
  • B83
  • Cβˆ’83
  • Dβˆ’38

Q13:

Given that 𝐴𝐡𝐢𝐷 is a trapezoid, where 𝐴𝐡βˆ₯𝐢𝐷, 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(6,βˆ’6)
  • B(1,βˆ’1)
  • C(βˆ’1,1)
  • D(βˆ’6,6)

Q14:

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 𝐴𝐡 and 𝐢𝐷 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 π‘₯-axis is .

Q17:

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?

  • Aπ‘₯=4
  • B𝑦=4
  • Cπ‘₯=βˆ’1
  • D𝑦=0
  • E𝑦=βˆ’1

Q18:

What is the value of 𝑏, if lines βˆ’2π‘₯+𝑏𝑦+6=0 and βˆ’π‘₯βˆ’4π‘¦βˆ’3=0 are parallel?

  • Aβˆ’8
  • Bβˆ’4
  • Cβˆ’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 (βˆ’1,0), and the line 𝐿 passes through the points (βˆ’3,2) and (0,βˆ’2). Are the two lines perpendicular?

  • Ano
  • Byes

Q21:

Let 𝐿 be the line through the points (βˆ’7,βˆ’7) and (βˆ’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 𝐡(4,βˆ’6) is perpendicular to the line passing through the points 𝐢(βˆ’9,19) and 𝐷(π‘₯,15), what is the value of π‘₯?

Q23:

The line on the points (10,π‘˜+2) and 𝐡(7,10) is parallel to one that makes an angle of 100∘ with the positive π‘₯-axis. Determine π‘˜ to the nearest integer.

Q24:

Two lines 𝐴 and 𝐡 have slopes of 89 and βˆ’1816 respectively. Are the two lines perpendicular?

  • AYes
  • BNo

Q25:

The line through points (βˆ’7,0) and (βˆ’2,𝑝) is perpendicular to the line βˆ’8π‘βˆ’4π‘₯+9=0. Find 𝑝.

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