#### Answer

$\left( \dfrac{5}{2},\dfrac{7\sqrt{3}}{2} \right)$

#### Work Step by Step

Using $\left( \dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2} \right)$ or the Midpoint Formula, the midpoint of the segment joining $\left(
9,2\sqrt{3}
\right) \text{ and } \left(
-4,5\sqrt{3}
\right),$ is
\begin{array}{l}\require{cancel}
\left( \dfrac{9+(-4)}{2},\dfrac{2\sqrt{3}+5\sqrt{3}}{2} \right)
\\\\=
\left( \dfrac{5}{2},\dfrac{7\sqrt{3}}{2} \right)
.\end{array}