# Given the coordinates of a single point on a circle and a length of an arc L, how do I find the coordinates of another point? Or, to put in another form: I have the radius r, the length of the arc L and (x_1,y_1) the coordinates. I need to express (x_2,y_2) using only r,L,x_1, and y_1.

Given the coordinates of a single point on a circle and a length of an arc $L$, how do I find the coordinates of another point?

Or, to put in another form: I have the radius $r$, the length of the arc $L$ and $\left({x}_{1},{y}_{1}\right)$ the coordinates. I need to express $\left({x}_{2},{y}_{2}\right)$ using only $r,L,{x}_{1}$, and ${y}_{1}$.

I'm at a dead end on this.
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seppegettde
Traveling along a fixed circle, is basically rotating a vector around a fixed point. For that we can use the well known rotation matrix $\left(\begin{array}{cc}\mathrm{cos}\theta & -\mathrm{sin}\theta \\ \mathrm{sin}\theta & \mathrm{cos}\theta \end{array}\right)$. But to succesfully do this you need to know the center of you circle first, like ccorn mentioned