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Line m is represented by the equation y - 1 = 3 y=-2²+1 Oy= 0 v= ²2 (²+1) □ v-1= ²3(²-1) Oy-1== (x + 5) 2 3x + 1 2 650 y= y= 2 1 3 3 2 (x + 1). Select all equations that represent lines perpendicular to line m. 3

Line m is represented by the equation y - 1 = 3 y=-2²+1 Oy= 0 v= ²2 (²+1) □ v-1= ²3(²-1) Oy-1== (x + 5) 2 3x + 1 2 650 y= y= 2 1 3 3 2 (x + 1). Select all equations that represent lines perpendicular to line m. 3

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Understanding Perpendicular Lines in Coordinate Geometry #### Problem Statement: Line \( m \) is represented by the equation \( y - 1 = -\frac{2}{3} (x + 1) \). Select **all** equations that represent lines perpendicular to line \( m \). #### Given Equations: 1. \( y = -\frac{3}{2}x + 1 \) 2. \( y = \frac{3}{2}(x + 1) \) 3. \( y - 1 = \frac{2}{3} (x - 1) \) 4. \( y - 1 = \frac{3}{2} (x + 5) \) 5. \( y = \frac{3x + 1}{2} \) 6. \( y = -\frac{2}{3} x + \frac{1}{3} \) #### Solution Explanation: A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. - The slope-intercept form of the given line equation \( y - 1 = -\frac{2}{3}(x + 1) \) can be simplified to identify the slope. The slope \( m \) is \(-\frac{2}{3}\). - Thus, the slope of any line perpendicular to it must be the negative reciprocal: \( \frac{3}{2} \). Next, we'll determine which of the given equations have the slope \( \frac{3}{2} \): 1. \( y = -\frac{3}{2}x + 1 \): - Slope = \(-\frac{3}{2}\) (Not perpendicular) 2. \( y = \frac{3}{2}(x + 1) \): - Slope = \(\frac{3}{2}\) (Perpendicular) 3. \( y - 1 = \frac{2}{3} (x - 1) \): - Slope = \(\frac{2}{3}\) (Not perpendicular) 4. \( y - 1 = \frac{3}{2} (x + 5) \): - Slope = \(\frac{3}{2}\) (Perpendicular) 5. \( y = \frac{3x + 1}{2} \): -
Transcribed Image Text:### Understanding Perpendicular Lines in Coordinate Geometry #### Problem Statement: Line \( m \) is represented by the equation \( y - 1 = -\frac{2}{3} (x + 1) \). Select **all** equations that represent lines perpendicular to line \( m \). #### Given Equations: 1. \( y = -\frac{3}{2}x + 1 \) 2. \( y = \frac{3}{2}(x + 1) \) 3. \( y - 1 = \frac{2}{3} (x - 1) \) 4. \( y - 1 = \frac{3}{2} (x + 5) \) 5. \( y = \frac{3x + 1}{2} \) 6. \( y = -\frac{2}{3} x + \frac{1}{3} \) #### Solution Explanation: A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. - The slope-intercept form of the given line equation \( y - 1 = -\frac{2}{3}(x + 1) \) can be simplified to identify the slope. The slope \( m \) is \(-\frac{2}{3}\). - Thus, the slope of any line perpendicular to it must be the negative reciprocal: \( \frac{3}{2} \). Next, we'll determine which of the given equations have the slope \( \frac{3}{2} \): 1. \( y = -\frac{3}{2}x + 1 \): - Slope = \(-\frac{3}{2}\) (Not perpendicular) 2. \( y = \frac{3}{2}(x + 1) \): - Slope = \(\frac{3}{2}\) (Perpendicular) 3. \( y - 1 = \frac{2}{3} (x - 1) \): - Slope = \(\frac{2}{3}\) (Not perpendicular) 4. \( y - 1 = \frac{3}{2} (x + 5) \): - Slope = \(\frac{3}{2}\) (Perpendicular) 5. \( y = \frac{3x + 1}{2} \): -
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