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: 6

Answer

The line through A and B is horizontal and has slope $m_{1}=0$. Any perpendicular line to it has undefined slope.
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Work Step by Step

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