Final answer:
The image of point T after a 180-degree rotation about the origin is (-7, 4), which is obtained by changing the signs of the original coordinates.
Step-by-step explanation:
The question is asking for the image of point T after a rotation of 180º about the origin. To find the image of a point after a 180-degree rotation, you change the sign of both the x and y-coordinates of that point. Point T has coordinates (7, -4). After rotating it 180 degrees about the origin, the x-coordinate changes from 7 to -7, and the y-coordinate changes from -4 to 4. Therefore, the image of point T after the rotation is (-7, 4).