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!