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Math Help - coordinate geometry help.

  1. #1
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    coordinate geometry help.

    rtsu is a quadrilateral where r(-1, -5), s(13, 9), q(3, -1), u(-2k, 3k), t(x, y).
    If k=2 and the slope of ts is -3/11 and sr is parallel to tu, find the coordinates of t.

    In the book there is a drawing of the quadrilateral but i dont know how to put drawing so please draw it yourselves and try, i dont know what to use to find t? i tried using perp. distance but it doesnt work.
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  2. #2
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    Quote Originally Posted by milan View Post
    rtsu is a quadrilateral where r(-1, -5), s(13, 9), q(3, -1), u(-2k, 3k), t(x, y).
    If k=2 and the slope of ts is -3/11 and sr is parallel to tu, find the coordinates of t.

    ...
    You already know the coordinates of 3 vertices of the quadrilateral:

    r(-1, -5), u(-4, 6), s(13,9)

    The slope of rs is:

    m_{r,s} = \dfrac{-5-9}{-1-13}=\dfrac{-14}{-14}=1

    Therefore the line through u parallel to rs has the equation:

    y-6=1\cdot (x-(-4))~\implies~\boxed{y=x+10}

    The line through s with the slope of m=-\dfrac3{11} has the equation:

    y-9=-\dfrac3{11}(x-13)~\implies~\boxed{y=-\dfrac3{11}x+\dfrac{138}{11}}

    The intersection of these 2 lines is point t:

    -\dfrac3{11}x+\dfrac{138}{11}=x+10~\implies~x=2

    Therefore t(2, 12)
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