Reflecting twice flips y, then x. Rotate 180° flips both again. Final A': (-4, 1).
Let's analyze the transformations step-by-step to find the final location of point A':
1. Reflection over the y-axis: This swaps the x-coordinate sign. Point A at (-4, 1) becomes (-4, -1).
2. Reflection over the x-axis: This swaps the y-coordinate sign. Now, A' is at (-4, 1).
3. Rotation by 180°: This flips the entire rectangle across the origin, meaning both x and y coordinates are negated. A' ends up at (4, -1).
Therefore, option (d) (-4, 1) is the correct answer for the final location of point A' after the sequence of transformations.
Here's a breakdown of why the other options are incorrect:
(a) (1, -1): This reflects A over the y-axis only, not the x-axis or rotating 180°.
(b) (1, 1): This reflects A over both axes but doesn't rotate 180°, resulting in a different location.
(c) (-4, -1): This reflects A only over the y-axis, not the x-axis or rotating 180°.