1. ## 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!

2. ## 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?