Final answer:
After rotating point A 180 degrees around the origin and reflecting it over the X-axis, the new location of point A is (2, 6).
Step-by-step explanation:
The student asked what the new location of point A at (-2,6) would be after rotating the point 180 degrees around the origin and then reflecting it over the X-axis. To solve this problem, we first apply the 180-degree rotation which changes the sign of both coordinates, turning (-2, 6) into (2, -6). The subsequent reflection over the X-axis will flip the Y-coordinate while leaving the X-coordinate unchanged, so the point (2, -6) becomes (2, 6). Therefore, the new location of point A after both transformations is option c, which is (2, 6).