https://file.aiquickdraw.com/mathbot/file/1725971486044aod6kvfm.jpg

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.

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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.

Two transformations are performed on Figure A to produce Figure B. Figure A and Figure B are similar, but not congruent. The first transformation is a reflection over a vertical line. Which transformation could be the second transformation?

Explore geometric transformations involving a reflection and dilation to find how Figure A transforms into Figure B. Understand how dilation affects size while preserving similarity, with solutions suitable for students in Grades 8-10.

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