https://file.aiquickdraw.com/mathbot/file/17277287724329pc39fgk.jpg

The question asks which sequence of transformations would result in a figure that is *similar*, but *not congruent*, to the original figure.

Key concepts:
- **Similarity** means the figure has the same shape but different size (scaled up or down).
- **Congruence** means the figure has both the same shape and size.
- **Dilation** changes the size, so a figure can be similar but not congruent to the original.

Let’s go through the options:

1. **Rotation about the origin of 25° followed by a dilation with a scale factor of 0.25**: 
   - A rotation preserves the shape and size.
   - Dilation by a factor of 0.25 reduces the size of the figure.
   - Since the dilation changes the size, the figure would be similar but not congruent.
   - **Correct**.

2. **Translation 3 units down followed by a dilation with a scale factor of 4**:
   - A translation moves the figure but doesn’t change its size.
   - Dilation by a factor of 4 increases the size of the figure.
   - The figure is similar but not congruent.
   - **Correct**.

3. **Translation 1 unit down followed by a reflection across the y-axis**:
   - Translation and reflection preserve both the shape and size of the figure.
   - There is no dilation or resizing, so the figure remains congruent.
   - **Incorrect**.

4. **Reflection across the x-axis followed by a rotation of 90° about the origin**:
   - Both reflection and rotation preserve both size and shape.
   - No resizing occurs, so the figure remains congruent.
   - **Incorrect**.

### Correct answers:
- Option 1 (rotation + dilation)
- Option 2 (translation + dilation)

Do you want any more details on this? Here are some questions to consider next:

1. How do you differentiate between congruent and similar transformations?
2. What effect does dilation have on figures in transformations?
3. Can a figure undergo multiple transformations and still be congruent?
4. How do reflections and rotations affect the size of a figure?
5. What are some real-world applications of similar transformations in geometry?

**Tip**: Remember, dilations always lead to similarity, not congruence, unless the scale factor is exactly 1.

Which sequence of transformations would result in a figure that is similar, but not congruent, to the original figure? Select all that apply.

Identify which sequence of transformations results in figures that are similar but not congruent. Explore key geometry concepts such as rotation, translation, reflection, and dilation. Suitable for Grades 8-10.

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