Question 1171383
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The problem  ASSUMES  that the points are in  "GENERAL  PLACEMENT",  which means that among the connecting lines

there are  NO  parallel lines and that the intersection points are  ALL  DIFFERENT  (there is no coinciding intersection points).



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In all, there are  8*7 different lines.


Every two different lines have one intersection point on the plane (inside  the strip between the lines or outside it).

The intersection points that lie on the given parallel lines are included in this counting.



Thus the number of intersection points is equal to the number of pairs of different lines,

which is the number of combinations of 56 lines taken 2 at a time  {{{C[56]^2}}} = {{{(56*55)/2}}} = 1540.    <U>ANSWER</U>


<U>ANSWER</U>.  The number of intersection points on the plane is  1540.

         The intersection points on the parallel lines are included.
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Solved.