Is it always, sometimes, or never true that the composition of two reflections results in the same image as a translation? Explain your reasoning.

Answer 1

Sometimes.

A translation preserves orientation so the orientation of the image is the same as that of the preimage.

Consider a square, side 1 unit, with vertices at 1,1 1,2 2,1 2,2

If you reflect this in the x and y axis the orientation of the image is same as the original square

If you reflect it in y = 2x the orientation will change