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

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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:

If the angle that a straight line makes with the positive 𝑥-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 𝑥-axis.

Q3:

Consider a line with slope 1 and another line that makes an angle of 45∘ with the 𝑥-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 (−7,−7) and (−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 ⃖⃗𝐴𝐵⟂⃖⃗𝐶𝐷 and the slope of ⃖⃗𝐴𝐵=25, find the slope of ⃖⃗𝐶𝐷.

  • A−52
  • B25
  • C−25
  • D52

Q6:

If 𝐴𝐵𝐶𝐷 is a parallelogram, where 𝐴(8,2) and 𝐵(−4,7), find the slope of ⃖⃗𝐷𝐶.

  • A512
  • B−512
  • C125
  • D−125

Q7:

Let 𝑀 be the line passing by the points (0,−8) and (−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 𝑥-axis? Give your answer to the nearest second.

  • A10231′44′′∘
  • B16728′16′′∘
  • C1231′44′′∘
  • D7728′16′′∘

Q8:

If the line that passes through the points 𝐴(6,0) and 𝐵(4,−6) is perpendicular to the line passing through the points 𝐶(−9,19) and 𝐷(𝑥,15), what is the value of 𝑥?

Q9:

If the line passing through points 𝐴(−13,8) and 𝐵(20,𝑦) is parallel to the line passing through points 𝐶(−2,0) and 𝐷(7,𝑦), what is the value of 𝑦?

Q10:

Given that 𝐴𝐵𝐶𝐷 is a trapezoid, where 𝐴𝐵∥𝐶𝐷, 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(−1,1)
  • D(−6,6)

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