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Let's solve Puzzle #5 step-by-step.

### Step 1: Reflect Point 2 over the line \( y = x \)
- Original Point 2: \( (-2, 2) \)
- Reflection over \( y = x \): Swap the coordinates, so it becomes \( (2, -2) \).

### Step 2: Rotate Point 3 by 90° clockwise around the origin
- Original Point 3: \( (-2, 3) \)
- 90° clockwise rotation formula: \( (x, y) \) becomes \( (y, -x) \).
- Applying this: \( (-2, 3) \) becomes \( (3, 2) \).

### Step 3: Rotate Point 1 by 180° around the origin
- Original Point 1: \( (0, 2) \)
- 180° rotation formula: \( (x, y) \) becomes \( (-x, -y) \).
- Applying this: \( (0, 2) \) becomes \( (0, -2) \).

### Step 4: Dilate Point 4 by a scale factor of 3 from the origin
- Original Point 4: \( (1, -1) \)
- Dilation by scale factor 3: Multiply both coordinates by 3.
- Applying this: \( (1, -1) \) becomes \( (3, -3) \).

### Summary of transformed points:
1. Point 2 after reflection: \( (2, -2) \)
2. Point 3 after rotation: \( (3, 2) \)
3. Point 1 after rotation: \( (0, -2) \)
4. Point 4 after dilation: \( (3, -3) \)

### Answer choices:
Now, let's match these transformed points with the options:

- A: \( (2, -3) \)
- B: \( (6, -1) \)
- C: \( (5, 1) \)
- D: \( (2, 5) \)
- E: \( (-2, -3) \)
- F: \( (3, 6) \)
- G: \( (6, 1) \)
- H: \( (1, -5) \)
- I: \( (5, -6) \)

Matching the points to the answer choices:

- \( (2, -2) \) doesn't directly match any option.
- \( (3, 2) \) matches option **F**.
- \( (0, -2) \) doesn't directly match any option.
- \( (3, -3) \) doesn't directly match any option.

Based on this, **F** is part of the answer, but we would need to review the process to fully match the correct points.

Solve a geometric puzzle involving reflections, rotations, and dilations of points on a coordinate plane. The puzzle asks to reflect, rotate, and dilate specific points, and then match the transformed coordinates to given answer choices.

This puzzle involves reflecting, rotating, and dilating points on a coordinate plane. Learn how to apply geometric transformation rules such as reflection over y = x, 90° and 180° rotations, and dilation by a scale factor. Suitable for Grades 8-10 students.

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