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.