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Math Help - abcd

  1. #1
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    abcd

    a (7,2) and c (1,4) are two vertices of a square abcd

    find in form ax + by = c the equation of the diagonal bd


    thanks
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  2. #2
    Super Member wingless's Avatar
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    First, find all the vertices.
    A(7,2)
    B(7,4)
    C(1,4)
    D(1,2)
    The diagonal |BD| has slope Dy/Dx.
    m = Dy/Dx = (2-4)/(1-7) = 1/3
    General line formula:
    y = mx + C
    y = 1/3x + C
    We know that the line will pass through B(7,4) and D(1,2).
    y = 1/3x + C
    4 = 1/3 7 + C
    C = 5/3
    So the equation becomes,
    y = 1/3x + 5/3
    3y = x + 5
    -x + 3y = 5

    ---------

    Edit: Aaaah the question was about a square, I thought it was a rectangle :S

    I don't have time to solve it at the moment, I think I can help you later..
    Last edited by wingless; February 17th 2008 at 03:42 AM.
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  3. #3
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    Hello, gracey!


    The center of the square is the midpoint of AC\!:\;O(4,3)

    The slope of AC is: . m_1 \:=\:\frac{2-4}{7-1}\:=\:-\frac{1}{3}

    Since the diagonals of a square are perpendicular,
    . . the slope of BD is: . m_2 \:=\:+3

    Now write the equation of the line through (4,3) with slope 3.

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