"Mike Schubert" <email@example.com> wrote in message news://firstname.lastname@example.org... > How it can be proved that for n>=3, n distinct points in the plane, > not all on a single line, determine at least n distinct lines ? >
Suppose that exactly k of the points lie on the same line for some k ( 2 <= k < n ). Then each of the remaining n - k points can be paired with each of these points leading to (n - k)*k distinct lines. Along with the first line this leads to 1 + (n-k)*k lines which is >= n for n >= 3.