https://file.aiquickdraw.com/mathbot/file/172662853559213pq9rwr.jpg

The problem in the image asks for the coordinates of the point \((-2, -3)\) after a 90° clockwise rotation about the center point \((3, -3)\).

### Steps to solve:

1. **Translation to the origin:**
   First, subtract the center coordinates from the point to translate the point to a coordinate system centered at \((3, -3)\). This will give us the relative coordinates of the point:
   \[
   (-2, -3) - (3, -3) = (-2 - 3, -3 - (-3)) = (-5, 0)
   \]
   So, the translated point is \((-5, 0)\).

2. **Rotation by 90° clockwise:**
   The formula for a 90° clockwise rotation of a point \((x, y)\) around the origin is:
   \[
   (x', y') = (y, -x)
   \]
   Applying this to the translated point \((-5, 0)\):
   \[
   (0, -(-5)) = (0, 5)
   \]
   So after rotation, the point is \((0, 5)\) in the translated system.

3. **Translation back to the original coordinates:**
   Now, we translate the point back to the original coordinate system by adding the center point \((3, -3)\):
   \[
   (0, 5) + (3, -3) = (0 + 3, 5 + (-3)) = (3, 2)
   \]

Thus, after rotating the point \((-2, -3)\) 90° clockwise around \((3, -3)\), the new coordinates are \((3, 2)\).

Let me know if you would like further explanation on any step!

### Related Questions:
1. What is the formula for a 180° rotation around a point?
2. How do you rotate a point 90° counterclockwise around the origin?
3. What changes in the formula for rotating around a different center, like \((2,1)\)?
4. How do you reflect a point over a given line, like \(y = x\)?
5. How do you translate a point by a vector in a 2D plane?

### Tip:
When rotating points around a center other than the origin, always remember to translate the center to the origin first, then perform the rotation, and finally translate back.

The point (-2, -3) is rotated 90° clockwise using center (-3, -3). Enter the coordinate of the image as (x, y).

Explore the steps to perform a 90-degree clockwise rotation of a point around a specific center in coordinate geometry. This problem uses the concept of rotation transformations to find the new position of a point on a coordinate grid.

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