https://file.aiquickdraw.com/mathbot/file/17267756712240lnq82un.jpg

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!

Determine the angles of rotation for the transformation of triangle ABC to A'B'C'.

Learn how to determine the angle of rotation for triangle ABC to A'B'C' about the origin. This problem involves key geometric concepts, including 90° clockwise and counterclockwise rotations on the coordinate plane. Suitable for students in Grades 8-10.

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