# Similar Triangles question

• October 24th 2012, 07:54 AM
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?