Answer
$6\sqrt{2} \text{ units}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Distance Formula to find the distance between the given points $\left(
\sqrt{2},\sqrt{6}
\right)$ and $\left(
-2\sqrt{2},4\sqrt{6}
\right)$.
$\bf{\text{Solution Details:}}$
With the given points, then $x_1=
\sqrt{2}
,$ $x_2=
-2\sqrt{2}
,$ $y_1=
\sqrt{6}
,$ and $y_2=
4\sqrt{6}
.$ 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{2}-(-2\sqrt{2}))^2+(\sqrt{6}-4\sqrt{6})^2}
\\\\
d=\sqrt{(\sqrt{2}+2\sqrt{2})^2+(\sqrt{6}-4\sqrt{6})^2}
\\\\
d=\sqrt{(3\sqrt{2})^2+(-3\sqrt{6})^2}
\\\\
d=\sqrt{9(2)+9(6)}
\\\\
d=\sqrt{18+54}
\\\\
d=\sqrt{72}
\\\\
d=\sqrt{36\cdot2}
\\\\
d=\sqrt{(6)^2\cdot2}
\\\\
d=6\sqrt{2}
.\end{array}
Hence, the distance is $
6\sqrt{2} \text{ units}
.$
