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.