Posts tagged 'proportions'

W.01 Planar Points, Line Proportions & Incidence Determinants

Over any field F of characteristic not equal to 2, a planar point is an ordered pair A = [x, y] and a planar line is a homogeneous 3-proportion l = <a : b : c> with (a, b) != (0, 0) representing a*x + b*y + c = 0; three points are collinear and three lines are concurrent if and only if their respective 3x3 coordinate determinants vanish.