Three points lie on a line when the area of the triangle they form is:

1. Three points that are not in a line enclose a genuine triangle. 2. If they are in a line the triangle collapses flat. 3. If the area of the triangle is zero, the three points are collinear. 4. So a zero area is the test for collinearity. _Source: syllabus Mathematics, Ch 9 'Straight Lines'_