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.
Through any two distinct points, exactly one straight line can be drawn. If you have more than two points, the number of lines that can be drawn depends on how many of those points are distinct and not collinear. For ( n ) distinct points, the maximum number of lines that can be formed is given by the combination formula ( \binom{n}{2} ), which represents the number of ways to choose 2 points from ( n ). If some points are collinear, the number of unique lines will be less.
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.
9
1
- 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.
There are 13*12/2 = 78 lines.
1 straight line. An infinite number of curved lines.
4*3/2 = 6 lines.
Through any two distinct points, exactly one straight line can be drawn. If you have more than two points, the number of lines that can be drawn depends on how many of those points are distinct and not collinear. For ( n ) distinct points, the maximum number of lines that can be formed is given by the combination formula ( \binom{n}{2} ), which represents the number of ways to choose 2 points from ( n ). If some points are collinear, the number of unique lines will be less.
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.