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

Yesenia Sherman 2022-06-29 Answered
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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Answers (1)

Colin Moran
Answered 2022-06-30 Author has 21 answers
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 )
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