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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.
One! That is what collinear means!
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64 triangles
8 collinear points determine 28 unique line segments
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.
It depends on where the dots are located. If they are all collinear only one straight line is required. For a 5x5 grid, only 5 lines are required.
It has 8. Each passes through the centre. Four pass through vertices, four pass through the mid-points of opposite sides. 4
THe maximum number of lines that can be achieved between 9 points is 8+7+6+5+4+3+2+1=36.
8. 4 between the opposite vertices 4 between the mid points of opposite sides.
8 points.
The correct answer is 76. There are 9 points in the grid. You can pick any 3 out of these 9 points in 9*8*7/(3*2*1) = 84 ways. However, 3 will form horizontal lines in the grid, 3 will form vertical lines in the grid, and 2 will form diagonal lines in the grid. None of these 8 triplets will form triangles, but all the rest will. So the answer is 84-8=76.
It has 8 parallal lines:)