Final answer:
The transformation that maps point A to A' and point B to B' is a reflection across the y-axis, as it changes the sign of the x-coordinate while maintaining the same y-coordinate for any given point.
Step-by-step explanation:
The coordinates given are A(3,3), A'(-3,3), B(4,-4), and B'(4,4). To determine which transformation maps A to A' and B to B', we need to analyze the changes in their coordinates. Point A is moved from (3,3) to (-3,3). Both points have the same y-coordinate but their x-coordinates are opposites of each other, which indicates a reflection across the y-axis. Similarly, point B is moved from (4,-4) to (4,4), which again shows that the y-coordinate has changed from negative to positive while the x-coordinate remains the same indicating a reflection across the x-axis.
The correct answer is B. Reflection across the y-axis. This transformation would change the sign of the x-coordinate while keeping the y-coordinate the same for any point, as observed with A and A'. B and B' are included to distract from the correct answer, as their transformation (a reflection across the x-axis) is not what is being asked regarding the mapping from A to A'.