Question 977217
to draw lines u have to select {{{2}}} points at a time (as no {{{3}}} are collinear)

thus number of selections of such points is:
 
{{{nC2= n!/ ( 2! (n-2)!)}}}....since you have {{{4}}} points, {{{n=4}}}, and we have

{{{4C2= 4!/ ( 2! (4-2)!)}}} 

{{{4C2= 4!/ ( 2! (2)!)}}} 

{{{4C2= (4*3*2*1)/ ( 2*1 (2*1))}}} 

{{{4C2= (4*6)/ 4}}} 

{{{4C2= 6}}}


{{{drawing( 600, 600, -10, 10, -10, 10, 
circle(1,1,.12),circle(1,5,.12),circle(-2,2,.12),circle(-3,5,.12),
line(1,10,1,-10),
graph( 600, 600, -10, 10, -10, 10, 5,-3x-4,-(1/3)x+4/3,-x+2)) }}}