m is at
[tex]m=\sqrt[]{2}-1[/tex]and n is at
[tex]n=3\sqrt[]{2}-5[/tex]Hence the midpoint is at
[tex]\text{midpoint}=\frac{n+m}{2}[/tex]by substituying the given values, we have
[tex]\text{midpoint}=\frac{(\sqrt[]{2}-1)+(3\sqrt[]{2}-5)}{2}[/tex]which is equal to
[tex]\begin{gathered} \text{midpoint}=\frac{\sqrt[]{2}-1+3\sqrt[]{2}-5}{2} \\ \text{midpoint}=\frac{3\sqrt[]{2}+\sqrt[]{2}-1-5}{2} \\ \text{midpoint}=\frac{4\sqrt[]{2}-6}{2} \\ \text{midpoint}=\frac{4\sqrt[]{2}}{2}-\frac{6}{2} \end{gathered}[/tex]hence, the answer is
[tex]\begin{gathered} \\ \text{midpoint}=2\sqrt[]{2}-3 \end{gathered}[/tex]