Answer
$(\sqrt 2, \frac{\sqrt 5}{2})$
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 $(\sqrt 2,3\sqrt 5)$ and $(\sqrt 2,-2\sqrt 5)$ will have a midpoint of $(\frac{\sqrt 2+\sqrt 2}{2}, \frac{3\sqrt 5+(-2\sqrt 5)}{2})=(\frac{2\sqrt 2}{2}, \frac{\sqrt 5}{2})=(\sqrt 2, \frac{\sqrt 5}{2})$.
