Final answer:
A 180° rotation around the origin negates the coordinates of a point. To find C′ after rotation, negate both coordinates of C. If original coordinates of C are unknown, they must be provided to calculate C′.
Step-by-step explanation:
The student's question pertains to the result of performing a 180° rotation around the origin on the vertices of triangle ABC, where the images of points A and B after rotation are given as A′(−1, 2) and B′(−4, 2). To find the image of point C after the same 180° rotation, we can apply the properties of rotations in the coordinate plane. When rotating a point 180° around the origin, the coordinates of the point are negated. This means if the original coordinates of point C are (x, y), then after the rotation, the coordinates of C′ will be (−x, −y).
To complete the student's answer, if the coordinates of point C are not provided, they must be given to calculate the image C′. However, if C already lies on the coordinate plane, we simply negate both the x and y coordinates to find the image of C after the rotation.