https://file.aiquickdraw.com/mathbot/file/1727230456775i1lo5ucw.jpg

In this problem, you're asked to rotate the figure 90° clockwise and then analyze the two statements:

### Step-by-Step Solution:

1. **Identifying Initial Coordinates**:
   - Point \( P \) is at (-7, 0).
   - Point \( Q \) is at (0, 0).
   - Point \( R \) is at (0, -4).

2. **Applying a 90° Clockwise Rotation**:
   - When rotating a point \( (x, y) \) 90° clockwise around the origin, the new coordinates become \( (y, -x) \).

   Let's apply this transformation to each point:
   - Point \( P(-7, 0) \) becomes \( P'(0, 7) \).
   - Point \( Q(0, 0) \) stays \( Q'(0, 0) \).
   - Point \( R(0, -4) \) becomes \( R'(4, 0) \).

3. **New Figure**:
   After rotating the figure, the new positions of \( P', Q', R' \) form a rotated shape on the graph.

### Evaluating the Statements:

- **Statement 1**: "The orientation of the figure did not change."
   - **False**: A 90° rotation changes the orientation of the figure.

- **Statement 2**: "The corresponding angle measures in the pre-image and image are congruent."
   - **True**: A rotation preserves angles, so the corresponding angles are congruent.

### Final Answers:
1. The orientation of the figure **did change** (False).
2. The corresponding angle measures are **congruent** (True).

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. What happens when you rotate a figure 180° clockwise?
2. How would you rotate a point counterclockwise by 90°?
3. Does rotation affect the size of the figure?
4. What transformation could you apply to achieve the same orientation without rotation?
5. How do reflections differ from rotations?

**Tip**: Always check how rotations change both the orientation and the coordinates of points systematically.

Rotate the figure 90° clockwise. Then, mark the statements as true or false.

Learn how to rotate a figure 90° clockwise and analyze the effects on orientation and angle congruence. This problem involves key coordinate geometry concepts and the formula for 90° rotations. Suitable for Grade 8 students.

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