CK-12 Geometry - Second Edition, Volume 1 of 2 by CK-12 Foundation

Author:CK-12 Foundation
Language: eng
Format: epub
Publisher: CK-12 Foundation

Slopes of Perpendicular Lines

Recall from Chapter 1 that the definition of perpendicular is two lines that intersect at a , or right, angle. In the coordinate plane, that would look like this:

If we take a closer look at these two lines, we see that the slope of one is -4 and the other is .

This can be generalized to any pair of perpendicular lines in the coordinate plane.

The slopes of perpendicular lines are opposite signs and reciprocals of each other.

Example 6: Find the slope of the perpendicular lines to the lines below.

a)

b)

c)

Solution: We are only concerned with the slope for each of these.

a) , so is the reciprocal and negative, .

b) , take the reciprocal and make the slope positive, .

c) Because there is no number in front of , the slope is 1. The reciprocal of 1 is 1, so the only thing to do is make it negative, .

Example 7: Find the equation of the line that is perpendicular to and passes through (9, -5).

Solution: First, the slope is the reciprocal and opposite sign of . So, . Now, we need to find the intercept. 4 is the intercept of the given line, not our new line. We need to plug in 9 for and -5 for to solve for the new intercept .

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