To determine the correct transformation that takes Figure A to Figure B, let's analyze the given options in relation to the figures on the graph.

Observations:

• Figure A is located in Quadrant IV (bottom-right) and Figure B is located in Quadrant II (top-left).
• It appears that Figure B is a rotation of Figure A. The relative positioning and shape are consistent with rotation.

Let's evaluate the transformation options:

1. A clockwise rotation of 270° about the origin:

   • A 270° clockwise rotation is equivalent to a 90° counterclockwise rotation. This would move Figure A from Quadrant IV to Quadrant I, which doesn't match the position of Figure B.

2. A reflection over the line $y = -x$:

   • Reflecting over the line $y = -x$ flips points across the diagonal that slopes downward from left to right. This would likely move Figure A to Quadrant II, where Figure B is. So, this seems like a strong candidate.

3. A reflection over the line $y = x$:

   • Reflecting over the line $y = x$ flips points across the diagonal sloping upward from left to right. This would not result in the observed transformation from Figure A to B.

4. A clockwise rotation of 180° about the origin:

   • A 180° rotation would place Figure A in Quadrant III, which is not where Figure B is located.

Conclusion:

The correct transformation is "A reflection over the line $y = -x$" because it moves the shape from Quadrant IV to Quadrant II and preserves the shape’s orientation as seen in Figure B.

Would you like further clarification on transformations, or do you have any specific questions? Here are five related questions that might help deepen your understanding:

1. What is the effect of reflecting over the line $y = x$ versus reflecting over $y = -x$?
2. How can you determine if a transformation is a rotation or a reflection?
3. What happens to coordinates of points during a 180° rotation about the origin?
4. Can you explain how to identify transformations visually on a graph?
5. How would a 90° clockwise rotation affect the position of Figure A?

Tip: To analyze transformations, it is often helpful to track the movement of specific points, like vertices, and observe how their coordinates change after the transformation.