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, 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

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

They are the same distance from point I
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.) (2 points)
0 / 10000 Word Limit
Question 3
What other point on the diagram would also be equidistant from points F and C? Explain how you know. (2 points)
0 / 10000 Word Limit
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Answer 1

a. They are the same distance from point I.

b. Because of the Perpendicular Bisector Theorem: any point on the perpendicular bisector of a segment is equidistant from the segment’s endpoints. (I is on the perpendicular bisector of FC, so IF = IC.)

c. Any other point on GH (for example point G or the midpoint where GH meets FC) is also equidistant from F and C. This is again because GH is the perpendicular bisector of FC, so every point on it is the same distance from F and C.