you can draw one segment to connect two points and three distinct segments to connect three named points. how many segments can you drawto connect five points if no three of the points lie on the same line.........please help me i am confused
A segment is created by joining any two points
So the question comes down to how many pairs of points can I form from 5 points.
This is a combination question
it would be 5choose 2 or C(5,2) = 10
Or
you could set up a pattern
points - lines
2 1
3 3 , an increase of 2
4 6 , an increase of 3
5 10 , and increase of 4 !!!! aha, there is the pattern
6 15 etc
To find out the number of segments you can draw to connect five points without any three of them lying on the same line, you can use a combinatorial approach.
First, let's consider connecting only two points at a time. To connect two distinct points, there is exactly one segment that can be drawn.
Next, let's consider connecting three distinct points. There are five points to choose from, and you need to choose three to connect. This can be calculated using the combination formula, denoted as C(n, r), which gives the number of ways to select r items from a set of n distinct items without regard to the order. In this case, C(5, 3) = 5! / (3! * (5-3)!) = (5 * 4) / (2 * 1) = 10.
Now, let's consider connecting four distinct points. There are five points to choose from, and you need to choose four to connect. Using the combination formula again, C(5, 4) = 5! / (4! * (5-4)!) = (5 * 4 * 3) / (1 * 3 * 2 * 1) = 5.
Finally, connecting all five distinct points would require drawing a line segment between each pair of points. In this case, we can calculate the number of line segments by using the formula:
nC2 = n! / (2! * (n-2)!)
Using n = 5, we get 5C2 = 5! / (2! * (5-2)!) = (5 * 4) / (2 * 1) = 10.
Therefore, the total number of line segments you can draw to connect five points without any three of them lying on the same line is:
1 (for connecting two points) + 10 (for connecting three points) + 5 (for connecting four points) + 10 (for connecting all five points) = 26.
Thus, you can draw 26 segments to connect five points without any three of them lying on the same line.