beninar6u

2022-09-05

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 ${y}_{1}$.

I'm at a dead end on this.

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 ${y}_{1}$.

I'm at a dead end on this.

seppegettde

Beginner2022-09-06Added 7 answers

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

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