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Prove that the product of a rotation and a translation is a rotation.

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Basic Math

Prove that the product of a rotation and a translation is arotation.

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4.1 Ratings (817 Votes)
Given rotation R and translation T neither of which are the identity show that TR must be a rotation My guess is that we can draw a triangle then rotate and translate it and then find some sort of intersection by extending lines from the triangles that is the center of the overall rotation but I dont think that works I assume you are working on the Euclidean plane We can then choose coordinates so that RR is rotation by angle in the counterclockwise direction measured in radians around the origin and TT is translation vector v v1v2vv1v2 A good representation for the plane is as the    See Answer
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