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, GH¯¯¯¯¯¯¯¯

Question

. 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.

a. Which pocket is closer?

(1 point)
Responses

They are the same distance from point I
Pocket C is closer to point I than Pocket F
Pocket C is closer to point I than Pocket F
Pocket F is closer to Point I than Pocket C

How do you know (either give the name of the theorem or write out what it says)

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

Answer 1

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.