Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - 2.1 Rectangular Coordinates and Graphs - 2.1 Exercises - Page 192: 19


a. $3\sqrt{41}$ b. $(0,\displaystyle \frac{5}{2})$

Work Step by Step

Let $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$. $d(P, Q)=\sqrt{(x_{2}-x_{\mathrm{I}})^{2}+(y_{2}-y_{1})^{2}}$ $M=(\displaystyle \frac{x_{\mathrm{I}}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$ ----------------------- a. $P(-6,-5), Q(6,10)$. $d(P, Q)=\sqrt{(6-(-6))^{2}+(10-(-5))^{2}}$ $=\sqrt{(12)^{2}+(15)^{2}}=\sqrt{144+225}=\sqrt{369}$ $=\sqrt{9\times 41}=3\sqrt{41}$ b. $M=(\displaystyle \frac{-6+6}{2},\frac{-5+10}{2})=(0,\frac{5}{2})$
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