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Math Help - Similar Triangles question

  1. #1
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    Question Similar Triangles question

    Hello! I am writing a program that requires some geometry and nothing I have found online gives me a clear answer...

    I have a point lets say at (3,2) I am animating moving that point to the origin at (0,0), and then back to (3,2). I understand that the side lengths will remain proportional to each other, but I can't figure out how I might be able create a sort of rate function I guess? To be able able to calculate the X and Y coordinates all along the path. I need to be able to manipulate each one of the somehow... the animation is continuously updating so I need to be able to decrement and increment the X and Y accordingly...

    any ideas?

    Thanks guys!
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Similar Triangles question

    The distance from the origin to a point at (x,y) is  r= \sqrt {x^2 + y^2}. Given that the point (3,2) is on the line that connects (3,2) to the origin, the equation of that line is y = (2/3)x. So the distance from the origin to any point on the line is r = \sqrt{x^2 + \frac 4 9 x^2} = \sqrt{\frac {13} 9} x =\frac { \sqrt{13} x} 3 . The rate at which 'r' changes is therefore equal to \frac {\sqrt {13}} 3 times the rate at which x changes. Is that what you're looking for?
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