Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Appendices - Section A.3 - Lines, Circles, and Parabolas - Exercises A.3 - Page AP-17: 5

Answer

The line through A and B has slope $m_{1}=3$. Any perpendicular line to it has slope $m_{2}=-\displaystyle \frac{1}{3}.$
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Work Step by Step

$A=(x_{1},y_{1})=(- 1, \ 2)$ $B=(x_{2},y_{2})=(-2, \ -1)$ The increments in the coordinates are calculated as $\left\{\begin{array}{l} \Delta x=x_{2}-x_{1}\\ \Delta y=y_{2}-y_{1} \end{array}\right.$ $\left\{\begin{array}{l} \Delta x=-2-(-1)=-1\\ \\ \Delta y=-1-2=-3 \end{array}\right.$ Slope of the line that passes through A and B, if the line is nonvertical, ($\Delta x\neq 0)$ is calculated as $m_{1}=\displaystyle \frac{\Delta y}{\Delta x}=\frac{-3}{-1}=3$, Any line perpendicular to the nonvertical line that passes through A and B has slope $m_{2}$, such that $m_{2}=-\displaystyle \frac{1}{m_{1}}=-\frac{1}{3}$
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