advertisement

Geometry 3.7 Perpendicular Lines in the Coordinate Plane Goals Use slope to identify perpendicular lines in a coordinate plane. Write equations of perpendicular lines. April 10, 2015 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 2 Review Lines are parallel if they have the same slope. Slope is rise/run. Lines with a positive slope rise to the right. Lines with a negative slope rise to the left. Horizontal Lines: slope = 0. Vertical Lines: slope is undefined (or none). Geometry 3.7 Perpendicular Lines in the Coordinate Plane 3 April 10, 2015 Problem Slopes Find the slope of the line containing (4, 6) and (2, 6). Do it graphically: m 66 42 0 0 2 Horizontal Lines have the form y = c. April 10, 2015 (2, 6) (4, 6) y=6 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 4 Problem Slope Find the slope of the line containing (4, 6) and (4, 3). Do it graphically: m 63 44 3 0 undefined (no SlopE) vertical Lines have the form x = c. April 10, 2015 (4, 6) (4, 3) x=4 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 5 Postulate 18 Two lines are perpendicular iff the product of their slopes is –1. Algebraically: m1 • m2 = –1 A vertical and a horizontal line are perpendicular. April 10, 2015 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 6 Example m1 1 m1 2 2 m2 2 1 -1 m1 m 2 2 1 2 2 1 m1 m2 m2 April 10, 2015 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 7 You don’t need a picture. Line A contains (2, 7) and (4, 13). Line B contains (3, 0) and (6, -1). Are the lines perpendicular? mA 13 7 42 6 3 2 1 (3) 1 3 April 10, 2015 mB 1 0 63 1 3 YES! Geometry 3.7 Perpendicular Lines in the Coordinate Plane 8 April 10, 2015 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 9 Exception Slope of m1 is ? Undefined m1 Slope of m2 is ? (2, 2) m2 (-2, 1) (3, 1) (2, -1) Zero m1 m2 –1. But m1 m2! A vertical line and a horizontal line are perpendicular. April 10, 2015 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 10 Another way to think of it: Two lines are perpendicular if one slope is the negative reciprocal of the other. 3 5 5 3 8 1 8 1 9 9 April 10, 2015 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 11 Slope Intercept form review y = mx + b m is the slope b is the y-intercept The y-intercept is at (0, b) Lines are parallel if they have the same slope. They are perpendicular if the product of their slopes is –1. April 10, 2015 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 12 More challenging problem p1 : 3 x 2 y 2 p2 : 2 x 3 y 2 These equations are in General Form Ax + By = C Slope is always: A B April 10, 2015 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 13 Why is this so? Consider the equation: 8x – 4y = 12 Move the 8x: – 4y = – 8x + 12 Divide by –4: y = 2x – 3 Slope is? 2 Now use –A/B: -8/(-4) = 2 April 10, 2015 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 14 For –3x + 2y = 2, slope is For 2x + 3y = –2, slope is A B A B 3 2 3 2 2 3 The slopes are negative reciprocals, so the lines are perpendicular. April 10, 2015 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 15 In summary Two lines are parallel if they have the same slope. Two lines are perpendicular if the product of their slopes is –1. General form is Ax + By = C and the slope in this form is –A/B. April 10, 2015 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 16 Homework April 10, 2015 Geometry 3.7 Perpendicular Lines in the Coordinate Plane 17