Given two points A and B, there is only one segment that you can name: AB. With three collinear points A, B, and C, there are three different segments that you can name: AB, AC, and BC. With five collinear points A, B, C, D, and E, how many different segments can you name?

Question

Given two points A and B, there is only one segment that you can name: AB.             With three collinear points A, B, and C, there are three different segments that you can name: AB, AC, and BC.  With five collinear points A, B, C, D, and E, how many different segments can you name?

anonymous · Answer

Using the network formula, we receive that:
$$
\#P=\frac{n^2-n}{2}
$$So, we plug in values for each necessary $n$.

anonymous · Answer

One example, we have 3 points:
$$
\#L=\frac{(3)^2-3}{2}=\frac{6}{2}=3
$$