The image shows a transformation of the triangle ABC to A'B'C'. Let's determine the type of transformation that has occurred.

The original points are:

• $A(-4, -2)$
• $B(-3, -1)$
• $C(-1, -2)$

The transformed points are:

• $A'(2, -4)$
• $B'(1, -3)$
• $C'(2, -1)$

Let's analyze the transformation step-by-step:

Checking Rotation:

1. Observe the movement of the points relative to the origin (0, 0).
2. Notice that the orientation of the figure has changed in a way that indicates a rotation.
3. Specifically, each point has been moved to a new location that is consistent with a 90° clockwise rotation about the origin.

To verify this, apply a 90° clockwise rotation formula:

• The transformation for a 90° clockwise rotation about the origin is: $(x, y) \to (y, -x)$

• Applying this to each point:

  • For $A(-4, -2)$: $(-4, -2) \to (-2, 4) = A'(2, -4)$
  • For $B(-3, -1)$: $(-3, -1) \to (-1, 3) = B'(1, -3)$
  • For $C(-1, -2)$: $(-1, -2) \to (-2, 1) = C'(2, -1)$

The transformation is a 90° clockwise rotation about the origin.

Conclusion:

The correct answer is:

"90° clockwise rotation about the origin".

Do you want more details or have any questions?

Here are some related questions you might find helpful:

1. How do you determine if a transformation is a reflection, rotation, or translation?
2. What is the difference between a 90° clockwise and a 90° counterclockwise rotation?
3. How can you apply rotation formulas to points without a graph?
4. What are the steps to determine the center of rotation for a given transformation?
5. How would you describe the transformation if the figure was rotated 180° instead?

Tip: When working with rotations, remember that rotating a point $(x, y)$ involves swapping and/or negating the coordinates depending on the direction and angle of the rotation.