Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 10 - Section 10.5 - Equations of Lines - Exercises: 23

Answer

$ -x+3y=2$

Work Step by Step

We find the slope of the original line: $m=\frac{-1-5}{5-3} = \frac{-6}{2}=-3$ The slope of the perpendicular line is the opposite reciprocal, which is 1/3. The line's midpoint is $(4,2)$, which is the average of the x and y endpoints. We obtain the equation, first using point slope form: $y-2 = 1/3(x-4) \\ 3y-6=x-4 \\ -x+3y=2$
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