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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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