Download presentation

Presentation is loading. Please wait.

Published byPaige Templeton Modified over 4 years ago

1
3.7 Perpendicular Lines in the Coordinate Plane Geometry Mrs. Spitz Fall 2005

2
Standard/Objectives: Standard 3: Students will learn and apply geometric concepts. Objectives: Use slope to identify perpendicular lines in a coordinate plane Write equations of perpendicular lines.

3
Assignment: Pp. 175-177 #7-45 and 47-50

4
Postulate 18: Slopes of Perpendicular Lines In a coordinate plane, two non- vertical lines are perpendicular if and only if the product of their slopes is -1. Vertical and horizontal lines are perpendicular

5
Ex. 1: Deciding whether lines are perpendicular Find each slope. Slope of j 1 3-1 = - 2 1-3 3 Slope of j 2 3-(-3) = 6 = 3 0-(-4) 4 2 Multiply the two slopes. The product of -2 3 = -1, so j 1 j 2 3 2

6
Ex.2 Deciding whether lines are perpendicular Decide whether AC and DB are perpendicular. Solution: Slope of AC= 2-(-4) = 6 = 2 4 – 1 3 Slope of DB= 2-(-1) = 3 = 1 -1 – 5 -6 -2 The product of 2(-1/2) = -1; so AC DB

7
Ex.3: Deciding whether lines are perpendicular Line h: y = ¾ x +2 The slope of line h is ¾. Line j: y=-4/3 x – 3 The slope of line j is - 4/3. The product of ¾ and - 4/3 is -1, so the lines are perpendicular.

8
Ex.4: Deciding whether lines are perpendicular Line r: 4x+5y=2 4x + 5y = 2 5y = -4x + 2 y = -4/5 x + 2/5 Slope of line r is -4/5 Line s: 5x + 4y = 3 5x + 4y = 3 4y = -5x + 3 y = -5/4 x + 3/5 Slope of line s is -4/5 -4 -5 = 1 5 4 The product of the slopes is NOT -1; so r and s are NOT perpendicular.

9
Ex. 5: Writing the equation of a perpendicular line. Line l 1 has an equation of y = -2x + 1. Find the equation of a line l 2 that passes through P(4, 0) and is perpendicular to l 1. First you must find the slope, m 2. m 1 m 2 = -1 -2 m 2 = -1 m 2 = ½ Then use m = ½ and (x, y) = (4, 0) to find b. y = mx + b 0 = ½(4) + b 0 = 2 + b -2 = b So, an equation of l 2 is y = ½ x - 2

10
Ex. 6: Writing the equation of a perpendicular line The equation y = 3/2 x + 3 represents a mirror. A ray of light hits the mirror at (-2, 0). What is the equation of the line p that is perpendicular to the mirror at this point? The mirrors slope is 3/2, so the slope of p is -2/3. Use m = -2/3 and (x, y) = (-2, 0) to find b. 0 = -2/3(-2) + b 0 = 4/3 + b -4/3 = b So, an equation for p is y = -2/3 x – 4/3

11
Coming Attractions: Chapter 3 Review – pp.180-182 #1-24. Chapter 3 Exam Chapter 4 Vocabulary Chapter 4: Postulates/ Theorems

Similar presentations

OK

GeometryGeometry 10.6 Equations of Circles Geometry Mrs. Spitz Spring 2005.

GeometryGeometry 10.6 Equations of Circles Geometry Mrs. Spitz Spring 2005.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on electrical network analysis Ppt on planet jupiter Ppt on political parties and electoral process Ppt on how to use powerpoint 2013 Ppt on applied operational research techniques Ppt on condition monitoring maintenance Ppt on world war first Ppt on linked list in java Ppt on if clauses in english grammar Best ppt on bluetooth technology