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.

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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&#039;m at a dead end on this.

seppegettde · Accepted Answer

Traveling along a fixed circle, is basically rotating a vector around a fixed point. For that we can use the well known rotation matrix       (                            cos          ⁡          θ                          −          sin          ⁡          θ                                      sin          ⁡          θ                          cos          ⁡          θ                      )  . But to succesfully do this you need to know the center of you circle first, like ccorn mentioned

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.

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