#### Answer

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

#### 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 $\left(
\sqrt{2},-1
\right) \text{ and } \left(
\sqrt{3},4
\right),$ is
\begin{array}{l}\require{cancel}
\left( \dfrac{\sqrt{2}+\sqrt{3}}{2},\dfrac{-1+4}{2} \right)
\\\\=
\left( \dfrac{\sqrt{2}+\sqrt{3}}{2},\dfrac{3}{2} \right)
.\end{array}