The question asks about the transformation that would map Figure A to Figure B, shown on a coordinate plane. Looking at the two figures, Figure A is in the fourth quadrant, while Figure B is in the second quadrant. Furthermore, Figure B appears to be rotated counterclockwise compared to Figure A.

To analyze the transformation:

1. Rotation: The figures seem related by rotation, not reflection. Specifically, a clockwise rotation by 270° around the origin would map Figure A to Figure B. This can be confirmed by observing the orientation of the shapes.

Let's review the given options:

• Reflection over the line $y = -x$: This would not map Figure A to Figure B, as reflections over this line would change both the position and orientation differently.
• Reflection over the line $y = x$: Similar to the previous reflection, this would not match the transformation.
• Clockwise rotation of 270° about the origin: This appears to be the correct transformation.
• Clockwise rotation of 180° about the origin: This would place Figure A in the opposite quadrant (third quadrant), so it is not correct.

Answer: The transformation that takes Figure A to Figure B is a clockwise rotation of 270° about the origin.

Would you like further details on this rotation or any other part of the problem?

Here are five related questions to consider:

1. How do rotations around the origin differ for different angles (90°, 180°, 270°)?
2. What is the effect of reflecting a shape over the line $y = -x$?
3. How can we calculate the coordinates of points after a 270° clockwise rotation?
4. Why is the clockwise direction significant in transformations?
5. How would a reflection differ from a rotation in terms of mapping figures?

Tip: Always check both the quadrant and orientation of the figures when determining the type of transformation.