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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 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

Pocket C is closer to point I than Pocket F
Pocket C is closer to point I than Pocket F
Question 2
b. How do you know? (Either give the name of the theorem or write out what it says) (2 points)
Because the theorem is the perpendicular bisector.

7 / 10000 Word Limit7 words written of 10000 allowed
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?

Responses:

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

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

Question 2

b. How do you know?

The theorem that applies here is the Perpendicular Bisector Theorem. This theorem states that any point on the perpendicular bisector of a line segment is equidistant from the endpoints of that segment. In this case, point I lies on the perpendicular bisector of segment FC, meaning that distance from point I to F is the same as the distance from point I to C.

Question 3

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

Another point that would be equidistant from points F and C is any point that lies on the line segment connecting F and C. This is due to the concept of reflection: when you reflect point I across the line segment FC, the resulting point would also be equidistant from both F and C. Additionally, any point along the perpendicular line to FC that is perpendicular and intersects it could also be used.