It is Geometry, isn't it? (Part 2)

First, let us try to find a generalized formula to this question.

A line is defined by atleast two points.Since, no three points are collinear, the problem becomes easier.

So, we need to find the total no. of combination of selecting two points. It is given by $^n C_2$ (combination)

Here n = no. of points = 7 So, $^7 C_2$ = 21

Thus, 21 lines are determined.

Let's solve an easier problem first by using 4 points.

There's a line connecting:

P1 and P2, P1, and P3, P1, and P4

P2, and P3, P2 and P4

P3, and P4

So 3 + 2 + 1.

Hopefully it is clear we can extend the same logic to 7 points.

6 + 5 + 4 + 3 + 2 + 1 = 21

There are 21 distinct lines determined.