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Math Help - show that a figure is a rhombus

  1. #1
    rcs
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    show that a figure is a rhombus

    Can anybody give me a hint what to do with this since there are no numbers given please.

    Let P,Q,R,S are the vertices of a parallelogram. Show, by analytic geometry, that if the diagonals are perpendicular the figure is a rhombus.

    thanks
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    Plot points at (0,0), (a,0), (b,c) and (a+b,c)

    The slope of one diagonal is \frac{c}{a+b}, and the slope of the other diagonal is \frac{c}{b-a}.

    Since the diagonals are perpendicular, \frac{c}{a+b}=\frac{a-b}{c}

    Solving for c yields c^2=a^2-b^2.

    Now use the distance formula to show that two adjacent sides have the same length.
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  3. #3
    rcs
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    im working on it now sir! thanks.
    God Bless
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