Question

What is the length of the mid segment 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. Thanks to whoever can help me!

Answer 1

(1) You can try to calculate length of AB, BC, CD, AD, AC, BD to make sure the order of vertices. (other way: you can plot them to see form of trapezoid and then find out positions of 4 vertices)

(2) From (1), identify 2 bases of trapezoid: AB and CD

=> Length of mid segment = (lengAB + lengCD)/2

=[ sqrt[(0-3)^2+(5-3)^2] + sqrt[(5-(-1))^2+(-2-2)^2] ]/2 = ~5.4

Other way

Define two points create mid segment P1 and P2

P1 is middle of AD = (A+D)/2 = (-0.5,3.5)

P2 is middle of BC = (B+C)/2 = (4,0.5)

=> Length of P1P2 = sqrt[(-0.5-4)^2+(3.5-0.5)^2] = 5.4