SOLUTION: prove the following using coordinate geometry: The segments joining the midpoints of the sides of a rectangle form a rhombus

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Question 1064274: prove the following using coordinate geometry: The segments joining the midpoints of the sides of a rectangle form a rhombus
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


Let the rectangle be ABCD with length L and width W,
with midpoints of sides E,F,G,H.  We are to show that 
EFGH is a rhombus.

We may then place the figure on a graph like this with
the coordinates as shown:



We us the distance formula to show that all the sides of EFGH have
the same length:









Since EF = FG = GH = HE, EFGH is a rhombus.

I didn't bother simplifying the length of the sides of rhombus EFGH,
but if you want to, it's



Edwin