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: 21


a. $\sqrt{133}$ b. $(2\displaystyle \sqrt{2},\frac{3\sqrt{5}}{2})$

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. $P(3\sqrt{2},4\sqrt{5}), Q(\sqrt{2},-\sqrt{5})$. $d(P, Q)=\sqrt{(\sqrt{2}-3\sqrt{2})^{2}+(-\sqrt{5}-4\sqrt{5})^{2}}$ $=\sqrt{(-2\sqrt{2})^{2}+(-5\sqrt{5})^{2}}=\sqrt{8+125}=\sqrt{133}$ b. $M=(\displaystyle \frac{3\sqrt{2}+\sqrt{2}}{2},\frac{4\sqrt{5}+(-\sqrt{5})}{2})=(2\sqrt{2},\frac{3\sqrt{5}}{2})$
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