How many lines are determined by n distinct points no 3 of which are collinear?

Question

asap really

how many lines are determined by n distinct points no 3 of which are collinear

Answer 1

To solve your problem, I'll begin by solving a slightly different one. Hopefully you can convince yourself that my work leads to the correct answer.

To begin, the formula for the number of diagonals in a convex n-gon is:

D = (n^2 - 3n) / 2

If we also include the line segments in the polygon's perimeter, we obtain:

L = (n^2 - 3n) / 2 + n

L = (n^2 - 3n) / 2 + 2n / 2

L = (n^2 - n) / 2

...where L is the number of unique lines determined by n points, no three of which are collinear. If two points determine a line, then, in the context of a polygon, that line can either be a side length or a diagonal. Hence, the number of diagonals plus the number of sides in a convex polygon is equivalent to the number of unique lines defined by those points.

EDIT: I gave you the formula. It's given by the equation:

L = (n^2 - n) / 2

Answer 2

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