Final answer:
The length of segment A'B' remains 2 centimeters after a 180-degree rotation about the origin and a translation of 3 units to the right, as neither transformation alters the segment's length.
Step-by-step explanation:
The question asks about the length of segment A'B' after segment AB has been rotated and translated. Since rotation about the origin does not change the length of a segment, AB will still be 2 centimeters long after the rotation. Following this, a translation (shifting the position without rotating or changing the size of the figure) 3 units to the right also does not alter the length of the segment. Thus, the length of segment A'B' remains the same as the length of segment AB, which is 2 centimeters.