Question

Find the exact length of the midsegment of trapezoid JKLM with verticesJ(6, 10), K(10, 6), L(8, 2), and M(2, 2).The length of the midsegment is

Answer 1

The midsegment is equal to the average of the lengths of the bases, so:

`M=(JM+KL)/(2)`

Where:

`\begin{gathered} JM=\sqrt[]{(6-2)^2+(10-2)^2} \\ JM=\sqrt[]{80}=4\sqrt[]{5}\approx8.9 \end{gathered}`

and

`\begin{gathered} KL=\sqrt[]{(10-8)^2+(6-2)^2} \\ KL=\sqrt[]{20}=2\sqrt[]{5}\approx4.47 \end{gathered}`

Therefore:

`M=\frac{4\sqrt[]{5}+2\sqrt[]{5}}{2}=3\sqrt[]{5}`