Answer
The given distance between the cities New Orleans and Houston is $328.5$ 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 New Orleans are $\left( {{x}_{1}},{{y}_{1}} \right)=\left( 8448,2625 \right)$.
The coordinates of Houston are $\left( {{x}_{2}},{{y}_{2}} \right)=\left( 8936,3542 \right)$.
Now compute the distance between the cities Boston and San Francisco as shown below:
$\begin{align}
& \sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}=\sqrt{{{\left( 8936-8448 \right)}^{2}}+{{\left( 3542-2625 \right)}^{2}}} \\
& =\sqrt{{{488}^{2}}+{{917}^{2}}} \\
& =\sqrt{238144+840889} \\
& =\sqrt{1079033}
\end{align}$
$=1038.765132$
So, the distance between the cities Boston and San Francisco is $1038.765132$ units, that is, $1038.765132\times \sqrt{0.1}\approx 328.5$ miles.
