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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)
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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3 answers

a. Since point I is on the perpendicular bisector of line segment FC, it means that point I is equidistant from points F and C. Therefore, the correct response is:

They are the same distance from point I.

b. 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. In this case, points F and C are the endpoints of segment FC, and point I lies on the perpendicular bisector, thus it is equidistant from both F and C.

c. Another point on the diagram that would also be equidistant from points F and C could be any point on the line segment connecting F and C itself or any point along the entire perpendicular bisector GH. This is because all points on the perpendicular bisector of a segment are equidistant from the segment's endpoints. Therefore, any point on line GH will also satisfy the condition of being equidistant from points F and C.

write the same thing but with very very simple words

a. Since point I is on the line that divides the line segment between F and C into two equal parts, it means point I is the same distance from F as it is from C. So, the answer is:

They are the same distance from point I.

b. The rule that helps us here is called the Perpendicular Bisector Theorem. It says that any point on the line that cuts a line segment in half at a right angle (perpendicular) is the same distance from both ends of that segment. Since point I is on this line, it is the same distance from points F and C.

c. Another point that is the same distance from F and C could be any point on the same line that cuts between them (the perpendicular bisector) or anywhere along that line. This is true because all points on this line are the same distance from the points F and C.