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: 20


a. $2\sqrt{17}$ b. $(5,2)$

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. $P(6,-2), Q(4,6)$. $d(P, Q)=\sqrt{(4-6)^{2}+(6-(-2))^{2}}$ $=\sqrt{(-2)^{2}+(8)^{2}}=\sqrt{4+64}=\sqrt{68}$ $=\sqrt{4\times 17}=2\sqrt{17}$ b. $M=(\displaystyle \frac{6+4}{2},\frac{-2+6}{2})=(5,2)$
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