Given the coordinates of rhombus wxyz are w 0, 4b, x 2a, 0, y 0, -4, and z -2, 0. prove the segments joining the midpoints of a rhombus from rectangle. as part of proof, find midpoint of xy

WXYZ is a rhombus with vertices W(0,4b), X(2a,0), Y(0,-4), Z(-2,0). You can see thap points W and Y lie on the y-axis and points X and Z lie on the x-axis. Then the centre of the rhombus is origin, thus W and Y are symmetric about the origin. Then b=1 and point W has coordinates (0,4). Similarly points X and Z are symmetric about the origin and a=1, hence X(2,0).

Let KLMN be middlepoints of segments WX, XY, YZ, ZW, respectively. Then .

Now find the vectors , , and :
that means that .

Similarly, ,, . 
You prove that KLMN is a recctangle.

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