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.
