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In this problem, you're asked to perform a 270° clockwise rotation of point \( A(1, -2) \) about the center of rotation, \( (-3, 3) \).

### Step-by-step solution:

1. **Translate the point to the origin**: 
   First, we translate both the center of rotation and the point by moving the center of rotation to the origin. To do this, subtract the coordinates of the center of rotation \( (-3, 3) \) from both the point \( A(1, -2) \) and itself.

   - The translated point will be:
   \[
   (1 - (-3), -2 - 3) = (1 + 3, -2 - 3) = (4, -5)
   \]
   
   - The center of rotation becomes \( (0, 0) \).

2. **Perform the 270° clockwise rotation**:
   To rotate a point \( (x, y) \) 270° clockwise around the origin, use the transformation formula:
   \[
   (x, y) \rightarrow (y, -x)
   \]
   So, applying this to the point \( (4, -5) \):
   \[
   (4, -5) \rightarrow (-5, -4)
   \]

3. **Translate the point back**:
   Now, undo the translation by adding back the coordinates of the original center of rotation \( (-3, 3) \):
   \[
   (-5 + (-3), -4 + 3) = (-5 - 3, -4 + 3) = (-8, -1)
   \]

### Final answer:
The image of point \( A \) after a 270° clockwise rotation about \( (-3, 3) \) is \( (-8, -1) \).

Would you like more details, or do you have any questions?

Here are some related questions you might find helpful:
1. What is the formula for rotating a point 90°, 180°, and 270° clockwise?
2. How do you perform rotations without translating to the origin first?
3. How does rotating a point differ from reflecting it?
4. What is the general rule for rotating around a point that is not the origin?
5. How do you verify the result of a geometric transformation?

**Tip**: When rotating a point, always remember to account for the center of rotation if it's not at the origin!

Using the pencil, plot the image of point A(1, -2) after a 270° clockwise rotation about (-3, 3).

This problem explains how to rotate point A(1, -2) by 270° clockwise around the point (-3, 3). Follow a step-by-step solution to translate, rotate, and reposition the point in a coordinate plane. Ideal for students in Grades 8-10 learning about geometric transformations.

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