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You've basically asked "what is 8 choose 2?", which is 8! / ( 6! * 2! ) or 28. The two are identical because each pair of points determines a line (since no three points are collinear). Since there are 28 ways to choose 2 items from a set of 8 items, there are 28 possible pairs of points and therefore 28 lines.
THe maximum number of lines that can be achieved between 9 points is 8+7+6+5+4+3+2+1=36.
The locus of points between 2 lines will always be another line that is halfway between the original 2 lines. In this case, that will be a line halfway between y=-2 and y=8, and since 3 is halfway between -2 and 8, the locus will be the line y=3.
Mutually perpendicular lines.