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

Draw an accurate picture of the trapezoid.

The parallel bases are clearly DC and AB.


The Distance formula between 2 points P(a, b) and Q(c, d) states that:


`|PQ|= \sqrt{ (a-c)^(2) + (b-d)^(2) }`


Using this formula we find:


`|AB|= \sqrt{ (0-3)^(2) + (5-3)^(2) }=√( 9+4)= √( 13)`


`|CD|= \sqrt{ (5-(-1))^(2) + (-2-2)^(2) }=√( 36+16)=√(52)=2√(13)=`


The length of the midsegment of a trapezoid is


`(|base_1|+|base_2|)/(2)= (√( 13)+2√( 13))/(2)= (3√(13))/(2)`


Answer:
`(3√(13))/(2)`