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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. Be sure to include the formulas.

  • geometry -

    Using the diagram and connecting the dots. The top horizontal line segment is y=b and the segment is the distance of the endpoints which is a-(-a) = 2a, the same goes for the bottom horizontal segment. The bottom is y=-b The vertical segments on the left and right would be x=-a (left side) and x=a on the right. The distance from the endpoints is b-(-b)=2b

    So the rectangle formed has the dimensions of 2a X 2b

    Since the lines are horizontal and vertical they form 90 degrees angles where they intersect. A characteristic of rectangle.

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