Given three distinct points labeled A, B, and C, how many different line segments can you draw using only these points?
1) 1
2) 2
3) 3
4) 4
To determine the number of different line segments that can be drawn using three distinct points labeled A, B, and C, we can use the formula for combinations.
Using the formula for combinations, "n choose r", where n is the total number of points and r is the number of points needed to form a line segment, we can calculate the number of line segments.
In this case, we have three points (A, B, C) and we need two points to form a line segment. So, the formula becomes "3 choose 2".
The formula for combinations is calculated as follows:
n! / (r! * (n - r)!), where "!" denotes factorial.
Let's calculate:
n! = 3! = 3 * 2 * 1 = 6
r! = 2! = 2 * 1 = 2
(n - r)! = (3 - 2)! = 1! = 1
Now, substitute the values into the formula:
3! / (2! * (3 - 2)!)
= 6 / (2 * 1)
= 6 / 2
= 3
Therefore, there are 3 different line segments that can be drawn using the given points A, B, and C.
So, the correct answer is 3) 3.