Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.9 - Distance and Midpoint Formulas; Circles - Exercise Set - Page 281: 71

Answer

The given distance between the cities Boston and San Francisco is $2,693$ miles.

Work Step by Step

The distance between two coordinates $\left( {{x}_{1}},{{y}_{1}} \right)\text{ and }\left( {{x}_{2}},{{y}_{2}} \right)$ is $\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}$. And the coordinates of Boston are $\left( {{x}_{1}},{{y}_{1}} \right)=\left( 4422,1241 \right)$. The coordinates of San Francisco are $\left( {{x}_{2}},{{y}_{2}} \right)=\left( 8495,8720 \right)$. Now, compute the distance between the cities Boston and San Francisco as shown below: $\begin{align} & \sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}=\sqrt{{{\left( 8495-4422 \right)}^{2}}+{{\left( 8720-1241 \right)}^{2}}} \\ & =\sqrt{{{4073}^{2}}+{{7479}^{2}}} \\ & =\sqrt{16,589,329+55,935,441} \\ & =\sqrt{72,524,770} \end{align}$ $=8516.147603$ So, the distance between the cities Boston and San Francisco is $8516.147603$ units, that is, $8516.147603\times \sqrt{0.1}\approx 2693$ miles.
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