3.7 Perpendicular Lines in the Coordinate Plane 1 GOAL

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Presentation transcript:

3.7 Perpendicular Lines in the Coordinate Plane 1 GOAL SLOPE OF PERPENDICULAR LINES 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.

Extra Example 2 Decide whether are perpendicular.

Checkpoint Line r goes through (–2, 2) and (5, 8). Line s goes through (–8, 7) and (–2, 0). EXAMPLE 3

Extra Example 3 Decide whether the lines are perpendicular. line a: line b: EXAMPLE 4

Extra Example 4 Decide 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.

3.7 Perpendicular Lines in the Coordinate Plane 2 GOAL 2 WRITING EQUATIONS OF PERPENDICULAR LINES EXAMPLE 5

Extra Example 5 Line 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?

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

What is the slope of the other line? QUESTION: The slope of one of two perpendicular lines is . a b What is the slope of the other line? ANSWER: _ b a