Answer
$(\frac{5\sqrt 2}{2}, \frac{5\sqrt 3}{2})$
Work Step by Step
We know that the midpoint of the line segment whose endpoints are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is the point with coordinates $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$.
Therefore, a line with endpoints $(\sqrt 8,-\sqrt 12)$ and $(3\sqrt 2,7\sqrt 3)$ will have a midpoint of $(\frac{2\sqrt 2+3\sqrt 2}{2}, \frac{-2\sqrt 3+7\sqrt 3}{2})=(\frac{5\sqrt 2}{2}, \frac{5\sqrt 3}{2})$.
We know that $\sqrt 8=\sqrt (4\times2)=\sqrt 4\times\sqrt 2=2\sqrt 2$.
Also, we know that $-\sqrt 12=-(\sqrt (4\times3))=-(\sqrt 4\times\sqrt 3)=-(2\sqrt 3)=-2\sqrt 3$.
