Posted by Cassidy on Sunday, September 18, 2011 at 1:17pm.
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
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