Showing Collinearity: Methods & Geometric Shapes

[dtl42]

What methods are there to show that three points are, or aren't collinear?

I know the standard, check the slopes stuff, but what other ways are there, I think there are some more obscure methods for geometric shapes right?

Thanks very much.

 

[matt grime]

if the points are P, Q and R, you can always wedge (i.e. take the vector product of) the vectors PQ and PR. The points will be colinear if and only if the wedge product is zero (i.e. the PQ and QR are parallel).

 

[HallsofIvy]

A straight line is the shortest distance between points. Calculate d(P,Q), d(P,R), d(Q,R), P, Q, and R are collinear if the sum of the two smaller distances is equal to the third distance.