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The image shows a grade 8 math assignment that involves analyzing transformations between two triangles, \( \triangle STU \) and \( \triangle S'T'U' \), on a coordinate plane. The question asks for the correct series of transformations that map triangle \( STU \) onto triangle \( S'T'U' \), with two options being correct.

### Analyzing the Transformations:
1. **Reflection across the x-axis**: This would flip triangle \( STU \) upside down. The triangle \( S'T'U' \) is indeed in a position that looks reflected across the x-axis.
2. **Rotation around the origin**: After the reflection, a rotation is required to map the points onto their final positions. Specifically:
   - A 180° counterclockwise rotation would map the triangle onto the correct orientation.
   - Alternatively, a 270° clockwise rotation would achieve the same result.

### Correct Options:
Based on the given choices:
- **Reflection across the x-axis followed by a 180° counterclockwise rotation about the origin** is correct.
- **Reflection across the x-axis followed by a 270° clockwise rotation about the origin** is also correct.

These transformations both result in mapping triangle \( STU \) to triangle \( S'T'U' \).

Would you like further details or have any specific questions?

### Related Questions:
1. How does a reflection across the y-axis differ from one across the x-axis?
2. What is the effect of a 90° rotation compared to a 180° rotation around the origin?
3. How can you determine the coordinates of a triangle after a series of transformations?
4. What are some other examples of composite transformations (reflection + rotation)?
5. How can we check whether two triangles are congruent after transformations?

### Tip:
When combining transformations, always apply them in the correct order as given, since order can affect the final position.

Which two series of transformations map triangle STU onto triangle S'T'U'?

Explore how reflections and rotations map triangle STU to S'T'U' in this Grade 8 math assignment. Learn about key transformation concepts, including reflections across the x-axis and rotations around the origin.

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