Final answer:
The coordinate of point D'(2, 4) after a 180° rotation about the origin is C. (-2, -4), since both the x and y coordinates are negated during such a rotation.
Step-by-step explanation:
When a point is rotated 180° about the origin in the Cartesian coordinate system, both the x and y coordinates are negated. The process changes the sign but not the magnitude of each coordinate. Therefore, if point D(2, 4) is rotated 180° around the origin, the new coordinates of D' would be (-2, -4). This is because each original coordinate is multiplied by -1. The correct answer to which coordinate D' would be after the rotation is option C. (-2, -4).