If the two lines are actually "on top of each other", they can have infinitely many points in common. If they are parallel, they have no points in common. If they are perpendicular, they have one point in common.
- If you're working on a single sheet of paper (2-D), then you can draw four lines that intersect in 1, 2, 3, 4, 5, or 6 points. - If in 3-D space, then you can also draw four lines that don't intersect at all.
4*3/2 = 6 lines.
4, 2 diagonal through the corners, 2 through the mid points of the sides
15 Consider one of the points. Call it point A. You can draw one line containing A through each of the other five lines (i.e., there are five lines that contain both A and another of the five points). Now, consider another of the points -- call it B. Excluiding the line that contains A and B, there are four lines that can be drawn containing B and one of the other four points. Continue this process for all the points. You get 5+4+3+2+1=15 lines. In general, if you have n non-collinear points, there are n+(n-1)+(n-2)+...+2+1=n*(n+1)/2 lines that can be drawn through any two of those points.
They are opposite parallel lines with points of (-2, 2) (2, 2) and (-2, -2) (2, -2)
9
- If you're working on a single sheet of paper (2-D), then you can draw four lines that intersect in 1, 2, 3, 4, 5, or 6 points. - If in 3-D space, then you can also draw four lines that don't intersect at all.
1
There are 13*12/2 = 78 lines.
1 straight line. An infinite number of curved lines.
4*3/2 = 6 lines.
2 lines, I believe.
The maximum is 10C2 = 10*9/(2*1) = 45
2 points
4, 2 diagonal through the corners, 2 through the mid points of the sides
15 Consider one of the points. Call it point A. You can draw one line containing A through each of the other five lines (i.e., there are five lines that contain both A and another of the five points). Now, consider another of the points -- call it B. Excluiding the line that contains A and B, there are four lines that can be drawn containing B and one of the other four points. Continue this process for all the points. You get 5+4+3+2+1=15 lines. In general, if you have n non-collinear points, there are n+(n-1)+(n-2)+...+2+1=n*(n+1)/2 lines that can be drawn through any two of those points.
They are opposite parallel lines with points of (-2, 2) (2, 2) and (-2, -2) (2, -2)