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Reflections and Translations

Any translation can be expressed as the composition of two reflections. In the sketch below, triangle A'B'C' is the result of translating triangle ABC by vector v. Triangle A''B''C'' is the result of reflecting triangle ABC over m followed by n. Play with the sketch, and decide how to compose  and  to produce a translation by dragging lines m and n until triangle A''B''C'' coincides with triangle A'B'C'. Is the composition unique?