Homework Help: Geometry :)

Posted by Bob on Tuesday, January 15, 2013 at 2:14pm.

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 :) - Steve, Tuesday, January 15, 2013 at 2:27pm
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 :) - Bob, Tuesday, January 15, 2013 at 3:10pm
Thanks :)

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