One.
Three lines are determined by three points unless the points are all on the same line ( i.e. co-linear)
Any three non-collinear points will define a single plane. A plane is composed of an infinite number of distinct lines.
In classical or Euclidean plane geometry two points defines exactly one line. On a sphere two points can define infinitely many lines only one of which will represent the shortest distance between the points. On other curved surfaces, or in non-Euclidean geometries, the number of lines determined by two points can vary. Even in the Euclidean plane, two points determine infinitely many lines that are not straight!
There are 13*12/2 = 78 lines.
3
3
4*3/2 = 6 lines.
depends on the position of the points if points are collinear, we have just only one line, the minimum number. If points are in different position (if any of the two points are not collinear) we have 21 lines (7C2), the maximum number of lines.
# 1
The smallest number of points of intersection of five lines drawn in a plane occurs when all the lines are parallel. In this case, the lines do not intersect at all, resulting in zero points of intersection. Thus, the smallest number of points of intersection is 0.
As long as at least two of them are different points, exactly one line.
The greatest number of intersection points with just four lines is 6.