To address the question, let's analyze the provided details carefully:

Given Information:

• Two transformations are performed on Figure A to produce Figure B.
• Figure A and Figure B are similar but not congruent (meaning their shapes are proportional but not identical in size).
• The first transformation is a reflection over a vertical line.

Question:

Which transformation could be the second transformation?

Options:

A. A reflection over a horizontal line
B. A translation to the right and down
C. A 270° counterclockwise rotation about a point on the figure
D. A dilation with a center at a point on the figure and a scale factor of 1
E. A dilation with a center at a point not on the figure and a scale factor of 3

Analysis:

1. Since Figure A and Figure B are similar but not congruent, the second transformation must change the size of the figure.

2. The first transformation, a reflection over a vertical line, does not alter the size; it only changes the orientation of the figure.

3. The second transformation should result in a size change, which leads us to suspect dilation as the type of transformation. This eliminates choices A, B, and C.

   • Dilation affects the size, making Figure B similar (but not congruent) to Figure A.

4. Option D suggests a dilation with a scale factor of 1, which does not change the size of the figure. Since Figure A and Figure B are not congruent, dilation with a scale factor of 1 would not create a size difference.

   • This eliminates Option D.

5. Option E suggests a dilation with a scale factor of 3, which increases the size of the figure. Since the two figures are similar but not congruent, this transformation fits the description of Figure A and Figure B. Therefore, the correct answer is likely Option E.

Conclusion:

The second transformation is likely E: A dilation with a center at a point not on the figure and a scale factor of 3.

Would you like further details or have any questions?

Here are five related questions to expand on this topic:

1. What is the difference between congruent and similar figures?
2. How does a reflection transformation affect a figure's orientation?
3. What does it mean to dilate a figure in geometry?
4. How can you distinguish between translations and rotations in transformations?
5. What are the properties of transformations that preserve congruence?

Tip: When performing geometric transformations, always consider whether the transformation changes size, orientation, or position to determine the type of transformation.