The midsegment is equal to the average of the lengths of the bases, so:
[tex]M=\frac{JM+KL}{2}[/tex]
Where:
[tex]\begin{gathered} JM=\sqrt[]{(6-2)^2+(10-2)^2} \\ JM=\sqrt[]{80}=4\sqrt[]{5}\approx8.9 \end{gathered}[/tex]
and
[tex]\begin{gathered} KL=\sqrt[]{(10-8)^2+(6-2)^2} \\ KL=\sqrt[]{20}=2\sqrt[]{5}\approx4.47 \end{gathered}[/tex]
Therefore:
[tex]M=\frac{4\sqrt[]{5}+2\sqrt[]{5}}{2}=3\sqrt[]{5}[/tex]
