If there are 10 points on a lone how many line segements does that make?
If the 10 points include the two endpoints,
then a line segment is identified by 2 points at a time
so the number is
C(10,2) = 45
e.g. suppose you label the points
A B C D ... J
then possible line segments are
AB
AC
AD
..
AJ
BC
BD
..
BJ
..
IJ
that is : 9+8+7+6+5+4+3+2+1 = 45