1. **State the problem:** We have quadrilateral STUV with vertices S(-5,7), T(-4,7), U(-2,1), and V(-8,1). We want to find the coordinates of these points after a 180° rotation about the origin. 2. **Formula for 180° rotation about the origin:** For any point $(x,y)$, the coordinates after a 180° rotation about the origin are given by: $$ (x', y') = (-x, -y) $$ This means we negate both the x- and y-coordinates. 3. **Apply the formula to each vertex:** - For $S(-5,7)$: $$ S' = (-(-5), -(7)) = (5, -7) $$ - For $T(-4,7)$: $$ T' = (-(-4), -(7)) = (4, -7) $$ - For $U(-2,1)$: $$ U' = (-(-2), -(1)) = (2, -1) $$ - For $V(-8,1)$: $$ V' = (-(-8), -(1)) = (8, -1) $$ 4. **Final answer:** The coordinates of the rotated quadrilateral STUV after a 180° rotation about the origin are: $$ S'(5, -7),\quad T'(4, -7),\quad U'(2, -1),\quad V'(8, -1) $$