To determine the angle of rotation from $\triangle ABC$ (blue triangle) to $\triangle A'B'C'$ (magenta triangle), we follow these steps:

Step 1: Recognize the rotation center.

• The problem states that the rotation is around the origin $(0, 0)$.

Step 2: Analyze corresponding points.

• Point $A$ rotates to $A'$, $B$ rotates to $B'$, and $C$ rotates to $C'$.

Step 3: Check the transformation visually:

• Triangle $ABC$ appears to rotate in a clockwise direction based on the relative positions of the triangles.
• The blue triangle ($\triangle ABC$) rotates down and to the right, indicating a clockwise rotation.

Step 4: Calculate the angle of rotation.

• A clockwise rotation of 90° about the origin maps the points to positions consistent with the image.

Conclusion:

The correct answer is 90° clockwise. So the answer is A: 90° clockwise.

Would you like more details about how to calculate rotations, or have further questions?

Here are 5 related questions for practice:

1. What happens to coordinates when rotated 180° about the origin?
2. How do we differentiate clockwise from counterclockwise rotations?
3. What is the formula for rotating a point 90° clockwise around the origin?
4. How does a rotation transformation affect the orientation of a figure?
5. What is the relationship between a 270° clockwise and a 90° counterclockwise rotation?

Tip: To confirm a rotation, track how one point on the shape moves from its original to its final position, as this often reveals the rotation angle easily!