1. **State the problem:** We need to find the coordinates of the point $R(3, 3)$ after it is rotated 180° clockwise around the origin. 2. **Formula and rules:** A rotation of 180° clockwise around the origin transforms any point $(x, y)$ to $(-x, -y)$. 3. **Apply the formula:** Original point: $R(3, 3)$ After 180° clockwise rotation: $$R' = (-3, -3)$$ 4. **Explanation:** Rotating 180° flips the point to the opposite quadrant, changing both $x$ and $y$ coordinates to their negatives. 5. **Final answer:** The coordinates of $R'$ are $(-3, -3)$.