The coordinates for a rhombus are given as (2a, 0), (0, 2b), (–2a, 0), and (0, –2b). Write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using coordinate geometry.
1 Answer
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Side1: (2a,0) to (0, 2b)
midpt: (a,b)
Side2: (0, 2b) to (-2a, 0)
midpoint: (-a,b)
Side3: (-2a, 0) to (0, -2b)
midpt: (-a, -b)
Side4: (0, -2b) to (2a, 0)
midpt: (a, -b)
So the mid points form a rectangle from -a to a in X, and from -b to b in Y.
Hope this helps!:)
