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: 22


a. $3\sqrt{55}$ b. $(2\displaystyle \sqrt{7},\frac{7\sqrt{3}}{2})$

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. $P(-\sqrt{7},8\sqrt{3}), Q(5\sqrt{7},-\sqrt{3})$. $d(P, Q)=\sqrt{(5\sqrt{7}-(-\sqrt{7}))^{2}+(-\sqrt{3}-8\sqrt{3})^{2}}$ $=\sqrt{(6\sqrt{7})^{2}+(-9\sqrt{3})^{2}}=\sqrt{36(7)+81(3)}$ $=\sqrt{9(4\cdot 7+9\cdot 3)}=3\sqrt{28+27}=3\sqrt{55}$ b. $M=(\displaystyle \frac{-\sqrt{7}+5\sqrt{7}}{2},\frac{8\sqrt{3}+(-\sqrt{3})}{2})=(2\sqrt{7},\frac{7\sqrt{3}}{2})$
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