1. **State the problem:** We need to find the coordinates of triangle $\triangle DEF$ after a rotation of 270° clockwise around the origin. The original vertices are $D(-9,-7)$, $E(-9,-1)$, and $F(-3,-7)$. 2. **Formula for rotation:** A rotation of 270° clockwise around the origin is equivalent to a 90° counterclockwise rotation. The formula for a 90° counterclockwise rotation of a point $(x,y)$ is: $$ (x,y) \to (-y, x) $$ 3. **Apply the rotation to each vertex:** - For $D(-9,-7)$: $$ (-9,-7) \to (-(-7), -9) = (7, -9) $$ - For $E(-9,-1)$: $$ (-9,-1) \to (-(-1), -9) = (1, -9) $$ - For $F(-3,-7)$: $$ (-3,-7) \to (-(-7), -3) = (7, -3) $$ 4. **Final answer:** The vertices of the rotated triangle $\triangle D'E'F'$ are: $$ D'(7,-9), E'(1,-9), F'(7,-3) $$ This completes the rotation of the triangle 270° clockwise around the origin.