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The question asks to determine the degree and direction of rotation that transforms the point \( P(-1, -2) \) to \( P'(2, 1) \).

### Step-by-step solution:

1. **Original Point**: \( P(-1, -2) \)
2. **New Point**: \( P'(2, 1) \)

We can analyze the points by visualizing or applying the properties of rotations around the origin.

- A **90° counterclockwise** rotation transforms \( (x, y) \) into \( (-y, x) \).
- A **180°** rotation transforms \( (x, y) \) into \( (-x, -y) \).
- A **270° counterclockwise** rotation (or 90° clockwise) transforms \( (x, y) \) into \( (y, -x) \).

Now, let’s check the options:

- **90° counterclockwise rotation**: \( (-1, -2) \) becomes \( (2, -1) \), but we need \( (2, 1) \), so this isn't correct.
- **180° rotation**: \( (-1, -2) \) becomes \( (1, 2) \), which is also not correct.
- **270° counterclockwise rotation**: \( (-1, -2) \) becomes \( (2, 1) \), which matches the new point.

Thus, the correct answer is a **270° counterclockwise rotation**.

Would you like any further details on this? 

Here are five related questions for practice:
1. How do you find the image of a point after a 90° counterclockwise rotation?
2. What is the difference between a clockwise and counterclockwise rotation in transformations?
3. How would you rotate a point 180° about the origin?
4. Can you describe how reflections differ from rotations?
5. What are the coordinates of \( (-3, 4) \) after a 270° clockwise rotation?

**Tip**: To easily visualize rotations, draw the points on a coordinate plane and trace the movement step by step!

The point P(-1, -2) is rotated to become P'(2, 1). Describe the rotation by degree and direction.

Explore how a 270° counterclockwise rotation transforms the point P(-1, -2) to P'(2, 1) with our step-by-step guide. This explanation covers rotation transformation formulas and the application of rotation matrix theory, suitable for students in Grades 8-10.

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