GOAL 1 SLOPE OF PERPENDICULAR LINES

3.7Perpendicular Lines in the Coordinate Plane

Slopes of Perpendicular Lines

•Two nonvertical lines are perpendicular if and only if the product of their slopes is –1.

•Vertical and horizontal lines are perpendicular.

EXAMPLE 1

Extra Example 1

Find each slope. Then find the product of the slopes.

EXAMPLE 2

Extra Example 2

Decide whether are perpendicular.

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Checkpoint

EXAMPLE 3

Line r goes through (–2, 2) and (5, 8). Line s goes through (–8, 7) and (–2, 0). Is ?r s

Extra Example 3Decide whether the lines are perpendicular.

line a: line b:2

13

y x 3

12

y x

EXAMPLE 4

Extra Example 4Decide whether the lines are perpendicular.line e: –2x + 7y = –4 line f : 7x + 2y = 10

Checkpoint

An equation for line v is An equation for line w

is 8x + 3y = 10.

3 5.

8 8y x

Is ?v w

GOAL 2 WRITING EQUATIONS OF PERPENDICULAR LINES

EXAMPLE 5

3.7Perpendicular Lines in the Coordinate Plane

Extra Example 5Line g has equation y = 3x – 2. Find the equation of the line h that passes through (3, 4) and is perpendicular to g.

EXAMPLE 6

Extra Example 6

The equation represents a mirror. A ray of light

hits the mirror at (3, 1). What is the equation of the line, p, that is perpendicular to the mirror at this point?

54

3y x

CheckpointFind an equation of the line that passes through Q(–2, 0) and is perpendicular to the graph of y = –2x + 4.

QUESTION:

The slope of one of two perpendicular lines is .ab

ANSWER:_ b a

What is the slope of the other line?