Show that three points lie on the same line 
Show that the points $A(3;9), B(-2;-16)$ and $C(0.2;-5)$ lie on the same line.

We can say that three points lie on the same line if the largest segment bounded by two of these points is equal to the sum of the smaller ones. Can you show me why this is sufficient for three points to lie on the same line?
By the distance formula, we can get $AB=\sqrt{650}, BC=\sqrt{125.84}$ and $CA=\sqrt{203.84}$. How to check if $AB=BC+CA$?


In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
source: https://en.wikipedia.org/wiki/Triangle_inequality


Thus, if $AB+BC=AC$, then the points must be on the same line.
