What other point on the diagram would also be equidistant from points F and C?

Question

Carlos is playing pool. He has 1 ball left to make in a pocket and then he will win. He knows that a pool table is a rectangle and there are 6 pockets that you can hit the balls into (indicated by points A, B, C, F, E, and D on the diagram below). In his head, he drew a line segment between points F and C and then pictured its perpendicular bisector, G HI. The ball he needs to hit is at point I, on the perpendicular bisector. He is trying to decide which pocket is closer, F or C.

Answer 1

To find another point on the perpendicular bisector of segment FC that is equidistant from both points F and C, we can consider the properties of the perpendicular bisector.

The perpendicular bisector of a segment is defined as the line that divides the segment into two equal parts at a right angle. Any point on this line is equidistant from the two endpoints of the segment (in this case, points F and C).

If point I is already identified as one such point, then any other point that lies on the line segment G HI (which represents the perpendicular bisector) will also be equidistant from points F and C.

To identify another point, you can choose any other point on this bisector line that is distinct from point I. For instance, if you move a distance along the bisector in either direction away from point I, you will find another point that is equidistant from F and C.

The exact coordinates of these points would depend on the specific geometry of points F and C and the perpendicular bisector's position in the diagram. However, the main conclusion is that any point on line segment G HI besides point I will be equidistant from points F and C.