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The problem involves determining the angle of clockwise rotation of triangle ABC around the origin. By analyzing the position of triangle \( ABC \) and its rotated version \( A'B'C' \), we can find the rotation angle.

Let me break down the steps for calculating the angle of rotation:

1. **Identify coordinates before and after rotation:**
   - Before rotation:
     - \( A = (1, 0) \)
     - \( B = (4, 6) \)
     - \( C = (0, 5) \)
   - After rotation:
     - \( A' = (0, -1) \)
     - \( B' = (-6, 4) \)
     - \( C' = (-5, 0) \)

2. **Calculate the angle of rotation:**
   We can find the angle of rotation by examining one point, say point \( A \), and its rotated image \( A' \). Since the origin is the center of rotation, the angle formed between the vector \( OA \) and \( OA' \) will give us the rotation angle.

Let me calculate this angle for you.The triangle \( ABC \) was rotated clockwise by **90 degrees** around the origin.

Would you like more details or have any questions?

Here are some related questions to deepen your understanding:
1. How would the coordinates change if the triangle were rotated counterclockwise by 90 degrees?
2. What would be the effect of a 180-degree rotation on the triangle's coordinates?
3. How do we apply matrix multiplication to find the new coordinates after rotation?
4. What is the geometric interpretation of a 270-degree clockwise rotation?
5. How can we generalize the formula to find the angle of rotation for any point?

**Tip:** When rotating points, always use the origin as the center unless stated otherwise, as it simplifies the computation.

How many degrees was triangle ABC rotated?

Learn how to determine the angle of rotation for triangle ABC rotated clockwise around the origin. This example uses coordinate geometry and the rotation matrix to find that the triangle was rotated 90 degrees. Suitable for students in Grades 8-10.

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