Help pleaseeeeeeeeeeeeeeee fast

Question

Given quadrilateral EFGH with vertices at E(-4,8), F(8,4), G(5, -5) and H(-7,-1), prove using coordinate geometry that EFGH is a rectangle. Note that there are a few different methods that work. 

Answer 1

E(-4,8), F(8,4), G(5, -5) and H(-7,-1)

EG = √9² + 13² = 5√10, FH = √15² + 5² = 5√10. So diagonals EG and FH equel, EG = FH.

Then midpoint of EG is (1/2, 3/2) and midpoint of FH is (1/2, 3/2) or the same point. So diagonals bysect each other. From here we can conclude that EFGH is rectangle.