3.7 Perpendicular Lines in the Coordinate Plane

Postulate 18“Slopes of Perpendicular Lines”

In a coordinate plane, 2 non-vertical lines are perpendicular if and only if the

product of their slopes is -1.

Vertical and Horizontal Lines are Perpendicular.

Example 1: Deciding whether the lines are perpendicular.

Line h: The slope of h is 3/4.

Line j: The slope of j is -4/3.

So the lines are perpendicular.

3 24

y x

4 33

y x

3 4 12 14 3 12

Example 2: Deciding whether the lines are perpendicular.

Line a: The slope of a is -2/3.

Line b: The slope of b is -3/2.

So the lines are NOT perpendicular. The Product needs to be -1.

2 13

y x

3 12

y x

2 3 6 13 2 6

Example 3: Deciding whether the lines are perpendicular.

Line r: Line s:

The product of the slopes is 1, not -1. So, r and s are not perpendicular.

4 5 2

5 4 24 25 5

45

x y

y x

y x

Slope

5 4 3

4 5 35 34 4

54

x y

y x

y x

Slope

Example 4: Find an equation of a perpendicular line.

Line t has an equation .

Find an equation of the line s that passes through P(4,0) and is perpendicular to t.

2 1y x

12

12102

Perpendicular Slope

y mx b

y x b