Answer
$\left(\dfrac{\sqrt2}{2},\dfrac{\sqrt5}{2}\right)$
Work Step by Step
The midpoint of the two points $(x_1,y_1)$ and $(x_2,y_2)$ is the point $\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$
$\left(\dfrac{\sqrt{2}+\sqrt2}{2},\dfrac{3\sqrt5-2\sqrt5}{2}\right) = \left(\dfrac{\sqrt2}{2},\dfrac{\sqrt5}{2}\right)$