Question 1050578
.
{{{(4*3)/2}}} = 6.


Each pair of points determines one line, a unique line.


So, the number of lines is equal to the number of pairs of points.


The number of pairs taken from the set of 4 points, is the number of combinations 
of four points taken 2 at a time: {{{C[4]^2}}} = {{{(4*3)/2}}} = 6.

On combinations, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A>

in this site.