document.write( "Question 1171383: Let $\"+l_1+\"$ and $\"+l_2+\"$ two parallel lines. We choose $\"+8+\"$ points on $\"+l_1+\"$ and $\"+7+\"$ on $\"+l_2+\"$ . Then all the market points on $\"+l_1+\"$ are joined with the market points on $\"+l_2+\"$ . How many points are obtained as an intersection (that are not in $\"+l_1+\"$ nor in $\"+l_2+\"$ ) of the traced segments?\r
\n" ); document.write( "\n" ); document.write( "I´ve solved the problem by doing all the lines and I got $\"+588+\"$ intersections, so, I´m looking for a solution with out making all of them. \n" ); document.write( "

Algebra.Com's Answer #796357 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "The problem ASSUMES that the points are in \"GENERAL PLACEMENT\", which means that among the connecting lines\r
\n" ); document.write( "\n" ); document.write( "there are NO parallel lines and that the intersection points are ALL DIFFERENT (there is no coinciding intersection points).\r
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document.write( "In all, there are  8*7 different lines.\r\n" );
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document.write( "Every two different lines have one intersection point on the plane (inside  the strip between the lines or outside it).\r\n" );
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document.write( "The intersection points that lie on the given parallel lines are included in this counting.\r\n" );
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document.write( "Thus the number of intersection points is equal to the number of pairs of different lines,\r\n" );
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document.write( "which is the number of combinations of 56 lines taken 2 at a time   =  = 1540.    ANSWER\r\n" );
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document.write( "ANSWER.  The number of intersection points on the plane is  1540.\r\n" );
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document.write( "         The intersection points on the parallel lines are included.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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