To determine which pocket is closer to point I on the perpendicular bisector GH of the segment FC, we rely on the property of perpendicular bisectors in geometry. The theorem that is relevant here is:
Perpendicular Bisector Theorem: Any point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment.
Since point I lies on the perpendicular bisector GH of segment FC, it must be equidistant from points F and C. This means the distance from point I to pocket F is the same as the distance from point I to pocket C.
The correct responses are: a. They are the same distance from point I. b. The reasoning is based on the Perpendicular Bisector Theorem.