Answer
We need 45 line segments to join each point for figure 2.
Work Step by Step
There are 10 points for figure 2.
We will now use combinations.
First of all, we need to find the number of combinations of 10 points chosen 2 at a time.
Find $10C_{2}$
Write using factorials:
$10C_{2}=\frac{10 !}{2!(10-2)!=\frac{10!}{2!8!}}$
Simplify:
$10C_{2}=45$
Therefore, we need 45 line segments to join each point.
