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To solve this problem, let's first identify how the trapezoid \( RSUT \) was reflected across the origin to produce \( R'S'U'T' \).

### Current Transformation:
- Reflecting across the origin means the coordinates of each point \( (x, y) \) on \( RSUT \) become \( (-x, -y) \). This is the transformation that has already been applied to create \( R'S'U'T' \).

Now, let's evaluate the other transformations one by one to determine which one **would not** produce \( R'S'U'T' \).

### Transformation Options:

1. **Reflecting across the x-axis, then reflecting across the y-axis**:
   - **Reflect across the x-axis**: \( (x, y) \) becomes \( (x, -y) \).
   - **Reflect across the y-axis**: \( (x, -y) \) becomes \( (-x, -y) \), which is exactly the same as reflecting across the origin.
   - **Conclusion**: This transformation would **produce** \( R'S'U'T' \).

2. **Rotating 180° about the origin**:
   - A 180° rotation about the origin transforms each point \( (x, y) \) into \( (-x, -y) \), which is also the same as reflecting across the origin.
   - **Conclusion**: This transformation would **produce** \( R'S'U'T' \).

3. **Rotating 90° clockwise about the origin, then reflecting across the y-axis**:
   - **Rotate 90° clockwise**: \( (x, y) \) becomes \( (y, -x) \).
   - **Reflect across the y-axis**: \( (y, -x) \) becomes \( (-y, -x) \), which is different from \( (-x, -y) \).
   - **Conclusion**: This transformation would **not produce** \( R'S'U'T' \).

4. **Reflecting across \( y = x \), then reflecting across \( y = -x \)**:
   - **Reflect across \( y = x \)**: \( (x, y) \) becomes \( (y, x) \).
   - **Reflect across \( y = -x \)**: \( (y, x) \) becomes \( (-x, -y) \), which is the same as reflecting across the origin.
   - **Conclusion**: This transformation would **produce** \( R'S'U'T' \).

### Final Answer:
The transformation that **would not** produce \( R'S'U'T' \) is:
- **Rotating 90° clockwise about the origin, then reflecting across the y-axis**.

Would you like more details or have any questions about this solution?

Here are 5 related questions you could explore:
1. What is the general formula for reflecting a point across the x-axis and y-axis?
2. How does a 90° clockwise rotation differ from a 90° counterclockwise rotation?
3. What is the formula for reflecting a point across the line \( y = x \)?
4. How would a reflection across \( y = -x \) affect a point's coordinates?
5. What are the properties of transformations that preserve congruence?

**Tip**: When performing multiple transformations, it's helpful to apply them step by step to check how each one affects the points.

Each point on the trapezoid RSUT was reflected across the origin to produce R'S'U'T'. Which other transformations would not produce R'S'U'T' from RSUT?

Explore which transformations would not produce R'S'U'T' from RSUT through reflections and rotations. Learn about geometric transformation concepts such as reflection across axes and rotations. Suitable for Grades 8-10.

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