To perform a 270° counterclockwise rotation about the origin, we can apply the following transformation to each point $(x, y)$:

$(x', y') = (y, -x)$

Applying this to each vertex:

1. Point A (2, -2): $A' = (-2, -2)$

2. Point B (-3, -2): $B' = (-2, 3)$

3. Point C (-1, 3): $C' = (3, 1)$

The coordinates of the vertices of triangle $A'B'C'$ after a 270° counterclockwise rotation are:

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

Let me know if you want more details or if you have any further questions.

Here are 5 related questions to deepen your understanding:

1. What would the coordinates be for a 90° counterclockwise rotation of the same triangle?
2. How do you calculate the area of triangle ABC using its vertices?
3. What are the rules for rotating a point by 180° about the origin?
4. Can you derive the formula for rotating a point by any arbitrary angle?
5. What are the reflection coordinates of the triangle over the x-axis?

Tip: When performing transformations, it's helpful to first visualize the triangle and confirm the new coordinates to ensure accuracy.