# Geometry :)

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

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

• Geometry :) -

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.

• Geometry :) -

Thanks :)

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