Label the points A,B,C
- A = (1,2)
- B = (4,5)
- C = (8,9)
Let's find the distance from A to B, aka find the length of segment AB.
We use the distance formula.
Segment AB is exactly units long.
Now let's find the distance from B to C
Segment BC is exactly units long.
Adding these segments gives
----------------------
Now if A,B,C are collinear then AB+BC should get the length of AC.
AB+BC = AC
Let's calculate the distance from A to C
AC is exactly units long.
Therefore, we've shown that AB+BC = AC is a true equation.
This proves that A,B,C are collinear.
For more information, check out the segment addition postulate.