Use coordinate geometry to prove that the quadrilateral formed by connecting the midpoints of a kite is a rectangle.

Question

I have no Idea how to do this problem, so if anyone could help I would be very greatfull. :)

Answer 1

Let the diagonals intersect at (0,0)
Then let the vertices of the kite be at

(-2a,0),(2a,0) and (0,2b),(0,-2c)

The midpoints of the sides are thus at
(a,b),(-a,b),(a,-c),(-a,-c)

Those are obviously the vertices of a rectangle.

Answer 2

Thanks :)