Lesson Worksheet: Slopes of Parallel and Perpendicular Lines Mathematics • 11th Grade

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:

If the angle that a straight line makes with the positive π‘₯-axis when measured counterclockwise is 0∘, what will the slope of the straight line be?

  • ANegative
  • BUndefined
  • CPositive
  • DZero

Q2:

Find, to the nearest two decimal places, the slope of the line that makes a positive angle of 60∘ with the positive direction of the π‘₯-axis.

Q3:

Consider a line with slope 1 and another line that makes an angle of 45∘ with the π‘₯-axis in a counterclockwise direction. Which of the following is correct about the two lines?

  • AThe two lines are perpendicular.
  • BThe two lines are parallel.
  • CThey are neither parallel nor perpendicular.

Q4:

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.

Q5:

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

Q6:

If 𝐴𝐡𝐢𝐷 is a parallelogram, where 𝐴(8,2) and 𝐡(βˆ’4,7), find the slope of ⃖⃗𝐷𝐢.

  • A512
  • Bβˆ’512
  • C125
  • Dβˆ’125

Q7:

Let 𝑀 be the line passing by the points (0,βˆ’8) and (βˆ’4,10), and 𝐿 the perpendicular to 𝑀 that passes through the origin (0,0). What is the measure of the positive angle that 𝐿 makes with the positive π‘₯-axis? Give your answer to the nearest second.

  • A10231β€²44β€²β€²βˆ˜
  • B16728β€²16β€²β€²βˆ˜
  • C1231β€²44β€²β€²βˆ˜
  • D7728β€²16β€²β€²βˆ˜

Q8:

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‘₯?

Q9:

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?

Q10:

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)

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