To find the coordinates of point \( T' \) after a 180-degree rotation about the origin, we can use the rotation mapping rule for a 180-degree rotation. The rule states that the coordinates \((x, y)\) of a point will be transformed to \((-x, -y)\).
Assuming the coordinates of point \( T \) before rotation are \((x, y)\), then after a 180-degree rotation, the coordinates of point \( T' \) would be:
\[ T' = (-x, -y) \]
Since you didn't provide the specific coordinates of point \( T \), you would need to substitute its coordinates into the transformation. For example, if \( T \) had coordinates \((3, 4)\), then:
\[ T' = (-3, -4) \]
If you can provide the coordinates for point \( T \), I can give you the exact coordinates for \( T' \).