Final Answer:
The correct sequence of transformations that will carry AABC onto AA'B'C' is a 180° clockwise rotation about the origin and a reflection about the y-axis. Therefore, the correct option is C.
Step-by-step explanation:
The sequence of transformations that will carry AABC onto AA'B'C' is a 180° clockwise rotation about the origin and a reflection about the y-axis. This is because a rotation of 180° will position A at A', B at B', and C at C', and the subsequent reflection about the y-axis will complete the transformation.
The other options involve translations, which only shift the positions of the points, and a rotation-reflection combination that would not match the desired transformation.
Therefore, the correct sequence for aligning AABC with AA'B'C' is a 180° clockwise rotation about the origin followed by a reflection about the y-axis.
Therefore, the correct option is C.