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 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)
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)
0 / 10000 Word Limit
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. 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)
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)
0 / 10000 Word Limit
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve this problem, let's analyze the situation step by step.
### Question 1:
**a. Which pocket is closer?**
Since point I lies on the perpendicular bisector (GH¯¯¯¯¯¯¯¯) of the segment connecting pockets F and C, point I is equidistant from both pockets F and C.
**Answer:**
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)**
The theorem that applies here is the **Perpendicular Bisector Theorem**, which states that any point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment. Therefore, since point I is on the perpendicular bisector GH¯¯¯¯¯¯¯¯ of segment FC, point I is equidistant from both points F and C.
**Answer:**
Perpendicular Bisector Theorem: Any point on the perpendicular bisector of a segment is equidistant from the segment's endpoints.
### Question 3:
**What other point on the diagram would also be equidistant from points F and C? Explain how you know.**
Any point on the line segment FC would be at varying distances from points F and C, but to find a point that is equidistant from F and C (just like point I), we can identify other points on the line that has a perpendicular bisector through I.
However, the primary point that can be guaranteed to be equidistant from F and C, besides I, is the midpoint of segment FC. This is because the midpoint of a line segment is defined as the point that divides the segment into two equal parts. It lies directly on the line joining F and C and is equidistant from both points.
**Answer:**
The midpoint of segment FC is also equidistant from points F and C, because it is the point that divides the segment into two equal lengths.
### Question 1:
**a. Which pocket is closer?**
Since point I lies on the perpendicular bisector (GH¯¯¯¯¯¯¯¯) of the segment connecting pockets F and C, point I is equidistant from both pockets F and C.
**Answer:**
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)**
The theorem that applies here is the **Perpendicular Bisector Theorem**, which states that any point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment. Therefore, since point I is on the perpendicular bisector GH¯¯¯¯¯¯¯¯ of segment FC, point I is equidistant from both points F and C.
**Answer:**
Perpendicular Bisector Theorem: Any point on the perpendicular bisector of a segment is equidistant from the segment's endpoints.
### Question 3:
**What other point on the diagram would also be equidistant from points F and C? Explain how you know.**
Any point on the line segment FC would be at varying distances from points F and C, but to find a point that is equidistant from F and C (just like point I), we can identify other points on the line that has a perpendicular bisector through I.
However, the primary point that can be guaranteed to be equidistant from F and C, besides I, is the midpoint of segment FC. This is because the midpoint of a line segment is defined as the point that divides the segment into two equal parts. It lies directly on the line joining F and C and is equidistant from both points.
**Answer:**
The midpoint of segment FC is also equidistant from points F and C, because it is the point that divides the segment into two equal lengths.
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