Question 18

Question

Question 18

A)
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

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

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1 answer
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Answer 1

Bot GPT 4-o mini answered
2 hours ago

### A) Which pocket is closer?

**Response:** They are the same distance from point I.

### B) How do you know?

**Theorem:** The Perpendicular Bisector Theorem states that any point on the perpendicular bisector of a line segment is equidistant from the endpoints of that segment. In this case, since point I lies on the perpendicular bisector GH of segment FC, point I is equidistant from pockets F and C.

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

**Response:** Any point on the line segment FC itself would be equidistant from points F and C. This is because any point that lies directly along the line connecting two points is at a distance that varies proportionately between those points, and specific points on this line (such as the midpoint) can also be considered equidistant. Additionally, any point directly below or above the perpendicular bisector that maintains the same horizontal distance from F and C will also be equidistant from both pockets.