I have something starting at (50, 10) it then rotates counter clockwise by 30 degrees, around the point at (50, 0), essentially mapping out an arc of a circle. How do I find the point it now lies on?

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Colin Moran · Accepted Answer

You apply a rotation matrix to the vector from the center of rotation to the point that is rotating. Here the vector is   (  50  −  50  ,  10  −  0  )  =  (  0  ,  10  ). Then you multiply that by       [                            cos          ⁡          θ                          sin          ⁡          θ                                      −          sin          ⁡          θ                          cos          ⁡          θ                      ]  , getting      [                            cos          ⁡          θ                          sin          ⁡          θ                                      −          sin          ⁡          θ                          cos          ⁡          θ                      ]        [                            0                                      10                      ]    =      [                            10          sin          ⁡                      30            ∘                                                10          cos          ⁡                      30            ∘                                ]    =      [                            5                                      5                      3                                ]  and add that to the center, getting   (  50  +  5  ,  0  +  5      3    )  =  (  55  ,  5      3    )

I have something starting at (50, 10) it then rotates

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