Final answer:
The correct compositions of two rigid motions mapping ΔABC to ΔA'B'C' are translation followed by rotation or rotation followed by translation.
Step-by-step explanation:
The compositions of two rigid motions that can map ΔABC to ΔA'B'C' could be a combination of a rotation followed by a translation, or vice versa. Therefore, the possible answers from the provided options are either a) Translation, rotation or b) Rotation, translation. Rigid motions such as reflection are also possible, but they would need to be followed by another motion, like translation, to achieve the correct orientation of the triangle.