Answer
$\left( \sqrt{3},-3\sqrt{6} \right)$
Work Step by Step
Using $\left( \dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2} \right)$ or the Midpoint Formula, then the midpoint of the line segment joing the given points, $
\left( \sqrt{3},-2\sqrt{6} \right) \text{ and }
\left( \sqrt{3},-4\sqrt{6} \right)
,$ is
\begin{array}{l}\require{cancel}
\left( \dfrac{\sqrt{3}+\sqrt{3}}{2},\dfrac{-2\sqrt{6}+(-4\sqrt{6})}{2} \right)
\\\\=
\left( \dfrac{\sqrt{3}+\sqrt{3}}{2},\dfrac{-2\sqrt{6}-4\sqrt{6}}{2} \right)
\\\\=
\left( \dfrac{2\sqrt{3}}{2},\dfrac{-6\sqrt{6}}{2} \right)
\\\\=
\left( \sqrt{3},-3\sqrt{6} \right)
.\end{array}
