Four points lie in the same plane, and each point can act as an endpoint. How many unique line segments can be formed using the set of points?

Question

A. eight

B. six

C. Five

D. Four

Answer 1

Here's another way to look at it, which boils down to the same things that Elias pointed out.

 

There are four points, so each point can be connected to the three other points.  That's 12 connections (4 x 3).

 

HOWEVER, if you stop there, you're counting every line segment twice.  That's because the line segment from point A to point B is the same as the one from B to A.  So to avoid double counting, you divide 12 by 2, to get 6.

 

Answer 2

By saying each point can act as an end point we are certain that the answer is 4 choose 2, which can be found as a numerical function on calculator, and even Google. The answer is 6, sort of like taking the points on the corners of a square drawing edges and diagonals (there it is also 6).