Answer
$\sqrt{103} \text{ units}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Distance Formula to find the distance between the given points $\left(
\sqrt{7},9\sqrt{3}
\right)$ and $\left(
-\sqrt{7},4\sqrt{3}
\right)$.
$\bf{\text{Solution Details:}}$
With the given points, then $x_1=
\sqrt{7}
,$ $x_2=
-\sqrt{7}
,$ $y_1=
9\sqrt{3}
,$ and $y_2=
4\sqrt{3}
.$ Using the Distance Formula which is given by $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}
,$ then
\begin{array}{l}\require{cancel}
d=\sqrt{(\sqrt{7}-(-\sqrt{7}))^2+(9\sqrt{3}-4\sqrt{3})^2}
\\\\
d=\sqrt{(\sqrt{7}+\sqrt{7}))^2+(9\sqrt{3}-4\sqrt{3})^2}
\\\\
d=\sqrt{(2\sqrt{7})^2+(5\sqrt{3})^2}
\\\\
d=\sqrt{4(7)+25(3)}
\\\\
d=\sqrt{28+75}
\\\\
d=\sqrt{103}
.\end{array}
Hence, the distance is $
\sqrt{103} \text{ units}
.$
