The image provided shows a problem that involves two geometric figures, labeled as Figure A and Figure B, on a coordinate plane. The task is to compare these figures.

Problem Analysis:

• Figure A appears in the first quadrant, and Figure B appears in the fourth quadrant.
• The shapes of the figures are identical, suggesting a transformation.

The question at the bottom is asking how Figure A and Figure B compare.

Answer Choices Explanation:

1. Option A: Figure A and Figure B are exactly the same with no transformation.
2. Option B: Figure A is a reflection of Figure B over the y-axis.
3. Option C: Figure A is a reflection of Figure B over the x-axis.
4. Option D: Figure A is a rotation of Figure B by 180 degrees about the origin.

Answer:

Given the position of the figures:

• Figure A is in the first quadrant (positive x and y coordinates).
• Figure B is in the fourth quadrant (positive x, negative y coordinates).

This suggests that Figure B is a reflection of Figure A over the x-axis.

Therefore, the correct answer is Option C: "Figure A is a reflection of Figure B over the x-axis."

Would you like further details on this explanation, or do you have any other questions?

Related Questions:

1. What are the key properties of reflections over the x-axis?
2. How do you determine the coordinates of a point after a reflection over the y-axis?
3. What is the effect of a 180-degree rotation about the origin on a figure’s coordinates?
4. How can you verify whether two figures are congruent after a transformation?
5. What is the difference between a reflection and