Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 2 - Functions and Their Graphs - Chapter Review - Cumulative Review - Page 117: 10


a) $\sqrt{29}$ b) $\left(\frac{1}{2},-4\right)$ c) $-\dfrac{2}{5}$

Work Step by Step

RECALL: (1) The distance $d$ from $P_1(x_1,y_1)$ to $P_2(x_2,y_2)$ is given by the formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. (2) The midpoint $M$ of the line segment from $P_1(x_1,y_1)$ to $P_2(x_2,y_2)$ is: $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$. (3) The slope $m$ of the line that passes through $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ is given by the formula $m=\dfrac{y_2-y_1}{x_2-x_1}$. Use the formulas above to obtain: a) $d=\sqrt{(3-(-2))^2+(-5-(-3))^2}=\sqrt{25+4}=\sqrt{29}$ b) $M=\left(\frac{-2+3}{2},\frac{-3+(-5)}{2}\right)=\left(\frac{1}{2},-4\right)$. c) $m=\dfrac{-5-(-3)}{3-(-2)}=\dfrac{-2}{5}$
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