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In R2, let C be any point. Let T_c : R2 --> R2 be the translation map T_c(P) = P + C.
(a.) Show T_c is a bijection by showing it is one to one and onto.
(b.) Show T_c is a bijection by finding its inverse.
(c.) Show T_c is distance preserving (using vectors).

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This solution demonstrates how to preserve distance.

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We have for any , where is a fixed point.
(a) I claim that is a bijection.
For any , if , then we ...

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