1. **Problem Statement:** We need to find the image of rectangle TUWV after a 180° counterclockwise rotation about the origin. 2. **Vertices of the original rectangle:** - T(5, 2) - U(8, 2) - W(5, 8) - V(8, 8) 3. **Rotation formula for 180° counterclockwise about the origin:** $$ (x, y) \to (-x, -y) $$ This means each point's coordinates are negated. 4. **Apply the rotation to each vertex:** - T(5, 2) becomes T'(-5, -2) - U(8, 2) becomes U'(-8, -2) - W(5, 8) becomes W'(-5, -8) - V(8, 8) becomes V'(-8, -8) 5. **Interpretation:** The rotated rectangle TUWV is now located in the third quadrant, with vertices at T'(-5, -2), U'(-8, -2), W'(-5, -8), and V'(-8, -8). 6. **Summary:** The 180° rotation about the origin negates both x and y coordinates of each vertex, effectively flipping the rectangle across the origin.