In this situation, since point I lies on the perpendicular bisector of the line segment connecting points F and C, we can conclude that the distances from point I to both points F and C are equal. This is based on the properties of a perpendicular bisector, which states that any point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment.
a. Which pocket is closer?
Response: They are the same distance from point I.
How do you know?
This can be explained by the Perpendicular Bisector Theorem, which states that any point lying on the perpendicular bisector of a segment is equidistant from the endpoints of that segment. Thus, point I is equidistant from points F and C.
What other point on the diagram would also be equidistant from points F and C?
Any point on the line segment connecting points F and C would also be equidistant from them, as well as any point on the perpendicular bisector itself (other than point I). This includes all the points along line GH that lies between points F and C, given that GH is the perpendicular bisector.