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Math Help - Finding Point along square's diagnal

  1. #1
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    Finding Point along square's diagnal

    Hello, Im stuck on a maths problem for an application im working on.
    I have made a diagram to explain. I have the x/y coordinates for the green dot, and need to then find the coords of the red dot. If sombody could direct me as to how to find this i would be very grateful.

    Finding Point along square's diagnal-2kewlc.jpg
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  2. #2
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    Re: Finding Point along square's diagnal

    Let (x0, y0) be the coordinates of the green dot. Assuming this is really a square (i.e., all sides are equal) and the origin is in the lower-left corner, the equation of the diagonal is y = x. The equation of the perpendicular to the diagonal that passes through the green dot is y - y0 = -(x - x0), i.e., y = -x + x0 + y0. Solving this system for x gives you x = (x0 + y0) / 2 = y.
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  3. #3
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    Re: Finding Point along square's diagnal

    Code:
    A                         B
          a
     
     b   P
     
                              x
     
     
     
     
    D           x             C
    If you want to have "real fun!", re-word your problem this way:
    Square ABCD has side lengths = x.
    Point P is inside, a from side AB, b from side AD.
    What is the distance from P to diagonal BD in terms of a,b,x?

    Spoiler:

    distance P to BD = SQRT(u^2 - v^2)
    where:
    u = SQRT[b^2 + (x-a)^2]
    v = (x + b - a) / SQRT(2)
    Last edited by Wilmer; September 16th 2011 at 03:42 PM.
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