Question

What is the length of the midsegment of the trapezoid made by the vertices A(0, 5), B(3, 3), C(5, -2) and D(-1, 2). Show equations and all work that leads to your answer.

Answer 1

help

Answer 2

AB has slope -2/3
CD has slope -2/3
They are the parallel sides
AB has distance \[\sqrt{9+4}\]
CD has distance \[\sqrt{36+16}=\sqrt{52}=2\sqrt{13}\]
The distance of the median is \[\frac {AB + CD}{2}\]=\[\frac {3\sqrt{13}}{2}\]