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anonymous

  • 4 years ago

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.

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  1. anonymous
    • 4 years ago
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  2. radar
    • 4 years ago
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    Your diagram is excellent, and shows that indeed the rectangle is formed. The width being 2a and the height being 2b.

  3. anonymous
    • 4 years ago
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    Thanks! Can you help me with the formulas?:)

  4. radar
    • 4 years ago
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    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

  5. radar
    • 4 years ago
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    So the rectangle formed has the dimensions of 2a X 2b

  6. radar
    • 4 years ago
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    Since the lines are horizontal and vertical they form 90 degrees angles where they intersect. A characteristic of rectangle.

  7. radar
    • 4 years ago
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    Thats all that I can come up with, hope it is enough.

  8. anonymous
    • 4 years ago
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    Yes, thank you so much!:) You've been such as big help!:)

  9. radar
    • 4 years ago
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    NP, good luck with your studies.

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