how many points of intersections are there?

Question

five lines are drawn on a piece of paper, no two of them are parallel, and not more than two lines intersecting a point. how many points of intersections are there? Show the ilustration of the five lines.

Answer 1

Each of the 5 lines will cross the other 4 at

a point.  None of the points of intersection

of any two lines match with the point of

intersection of one of the others.

 

Line 1:  4 points of intersection....

(L1,L2), (L1,L3), (L1,L4), (L1,L5)

 

Looking at Line 2, it also crosses the other

4 lines, but the point of intersection with

Line 1 is already accounted for... Thus

there are 3 more points of intersection.

 

The same logic applies with the other 3 lines

 

Points of intersection:  4 + 3 + 2 + 1 + 0 = 10