1. Millburn Academy
Maths department
Higher
Collinearity

2. Definition:
Three or more points are said to be collinear if they lie on a straight line.
Example 1
K is (-2, 6) L is (5, -8), and M is (9, -16). Prove that the three points are collinear.
KL & LM have equal gradients so they are parallel.
Point L is a common point so it follows that K, L & M are collinear. K L L M

3. Example 2
A Navy jet flies over two lighthouses with map coordinates (210,115) & (50,35). If it continues on the same path will it pass over a yacht at (10,15) ?
Since gradients are equal the lines joining the points are parallel & (50,35) is a common point then the three places are collinear so plane must fly over all three.