1. **State the problem:** We have a rectangle with vertices A(-3, -3), B(1, -3), C(1, -5), and D(-3, -5). We need to find the coordinates of the image after rotating the rectangle 270 degrees clockwise about the origin. 2. **Formula for rotation:** To rotate a point $(x,y)$ by 270 degrees clockwise about the origin, we use the transformation: $$ (x,y) \to (y, -x) $$ This is because a 270-degree clockwise rotation is equivalent to a 90-degree counterclockwise rotation. 3. **Apply the rotation to each vertex:** - For A(-3, -3): $$ (x,y) = (-3,-3) \to (y,-x) = (-3,3) $$ - For B(1, -3): $$ (x,y) = (1,-3) \to (y,-x) = (-3,-1) $$ - For C(1, -5): $$ (x,y) = (1,-5) \to (y,-x) = (-5,-1) $$ - For D(-3, -5): $$ (x,y) = (-3,-5) \to (y,-x) = (-5,3) $$ 4. **Final answer:** The coordinates of the image after a 270-degree clockwise rotation are: $$ A'(-3,3), B'(-3,-1), C'(-5,-1), D'(-5,3) $$