Practice Perpendicularity in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Lines, segments, or planes that intersect at exactly a right angle of 90°90° to each other.

The corner of a book or a room—the two edges meet at precisely 90°90°.

Showing a random 20 of 50 problems.

Example 1

medium
True or false: The diagonals of every rectangle are perpendicular.

Example 2

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Find the slope perpendicular to the line through (2,1)(2, 1) and (6,9)(6, 9).

Example 3

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Line 2x−5y=102x - 5y = 10 has what slope? What slope is perpendicular?

Example 4

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A perpendicular bisector of a segment does what to the segment?

Example 5

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Write the equation of the line through (1,2)(1, 2) perpendicular to y=3x+4y = 3x + 4.

Example 6

challenge
Why does the perpendicular distance give the SHORTEST distance from a point to a line?

Example 7

easy
Are lines with slopes 2 and −2-2 perpendicular?

Example 8

easy
A square has perpendicular sides. How many right angles does it have?

Example 9

challenge
Given line ℓ:4x+3y=12\ell: 4x + 3y = 12, find the equation of the line perpendicular to ℓ\ell through the point where ℓ\ell crosses the xx-axis.

Example 10

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A right triangle's legs are perpendicular. If one leg lies along a line of slope 4, what is the slope of the other leg?

Example 11

easy
Two lines have slopes 3 and −13-\tfrac{1}{3}. Are they perpendicular?

Example 12

challenge
Find the equation of the perpendicular bisector of the segment from (2,1)(2, 1) to (6,5)(6, 5).

Example 13

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Is the line y=5xy = 5x perpendicular to 5y=−x5y = -x?

Example 14

easy
Line ℓ1:y=2x+1\ell_1: y = 2x + 1. Write the equation of a line ℓ2\ell_2 perpendicular to ℓ1\ell_1 that passes through (4,3)(4, 3).

Example 15

hard
Find the foot of the perpendicular from point P(3,7)P(3, 7) to the line ℓ:y=2x−1\ell: y = 2x - 1.

Example 16

easy
Two roads meet at right angles. What is the angle between them in degrees?

Example 17

hard
In the quadrilateral with vertices A(0,0)A(0,0), B(4,0)B(4,0), C(4,3)C(4,3), D(0,3)D(0,3), are sides ABAB and BCBC perpendicular?

Example 18

easy
At what angle do perpendicular lines meet?

Example 19

challenge
Two lines are perpendicular and pass through (2,5)(2, 5). One has slope 23\tfrac{2}{3}. Find the xx-intercept of the other.

Example 20

easy
Line mm passes through (0,−1)(0, -1) with slope 35\dfrac{3}{5}. Write the equation of the line perpendicular to mm through the origin.
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