1. The problem states that triangle T is rotated 180° about the origin to form triangle T'. 2. The coordinates of vertex A of triangle T are given as (4, 7). 3. A 180° rotation about the origin transforms any point $(x, y)$ to $(-x, -y)$. 4. Applying this to vertex A: $A' = (-4, -7)$. 5. Therefore, the coordinates of vertex A' after the rotation are $(-4, -7)$.