[**Complete quadrilateral. Def.** Let OACB be any quadrilateral. Let AC and OB be produced to meet in E, and BC and OA to meet in F. Join AB, OC, and EF. The resulting figure is called a complete quadrilateral ; the lines AB,OC, and EF are called its diagonals, and the points E, F, and D (the intersection of AB and OC) are called its vertices.]
Take the lines OAF and OBE as the axes of x and y.
Let OA = 2a and OB = 2b, so that A is the point (2a, 0) and B is the point (0, 2b); also let C be the point (2h, 2k).
Then L, the middle point of OC, is the point (h, k), and M, the middle point AB is (a, b)
The equation to LM is therefore
These coordinates clearly satisfy (1), i.e., N **** on the straight line LM.
