It is sufficient because if three points lie are collinear then there is a middle point, say $M$ and there are two end points, say $E_1$ and $E_2$, then
$$E_1E_2=E_1M+E_2M$$
It is same as saying that if your school lies midway between your home and police station, then the distance between your home and police station is the sum of the distances between your home and school and your school and police station.
For your second question,
$$BC=\sqrt{125.84}\\
=0.1\times\sqrt{12584}\\
=0.1\times2\times11\times\sqrt{26}\\
=2.2\sqrt{26}$$
Similarly,
$$CA=2.8\sqrt{26}$$
and
$$AB=5\sqrt{26}$$
Also, there are easier ways to check that three points are collinear, for example note that three points are collinear iff the area of the triangle formed by them is zero, i.e.
$$\begin{vmatrix}
3&9&1\\
-2&-16&1\\
0.2&-5&1
\end{vmatrix}=0$$
Another easy method is that all of them satisfy the linear equation $5x-y=6$, hence they are collinear.