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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.

Which transformation would take Figure A to Figure B?

Discover how to transform Figure A to Figure B using a 270° clockwise rotation about the origin. This geometry problem involves analyzing rotations and reflections. Suitable for students in Grades 8-10.

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