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Question 1

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¯¯¯¯¯¯¯¯
. 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

Pocket C is closer to point I than Pocket F
Pocket C is closer to point I than Pocket F

They are the same distance from point I
They are the same distance from point I

Pocket F is closer to Point I than Pocket C
Pocket F is closer to Point I than Pocket C
Question 2
b. How do you know? (Either give the name of the theorem or write out what it says) (2 points)
0 / 10000 Word Limit
Question 3
What other point on the diagram would also be equidistanct from points F and C? Explain how you know. (2 points)

1 answer

Question 1

a. Which pocket is closer?

Response: They are the same distance from point I.

Question 2

b. How do you know? (Either give the name of the theorem or write out what it says)

Response: This is a consequence of the Perpendicular Bisector Theorem, which states that any point on the perpendicular bisector of a line segment is equidistant from the endpoints of that segment. Since point I lies on the perpendicular bisector of segment FC, it is equidistant from both points F and C.

Question 3

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

Response: Another point that would be equidistant from points F and C would be any point that lies on the line segment connecting F and C itself. This includes the midpoint of segment FC, as well as any point directly above or below the line segment, as long as those points are also on the perpendicular bisector. We know this because the Perpendicular Bisector Theorem ensures that all points along this bisector maintain equal distance to both endpoint F and endpoint C.