Question

Show that the points $(2,3),(3,1)$ and $(1,5)$ are collinear.

Answer 1

If the given points are collinear, then
$\left|\begin{array}{ccc}2& 3& 1\\ 3& 1& 1\\ 1& 5& 1\end{array}\right|=0$

$\left|\begin{array}{ccc}2& 3& 1\\ 3& 1& 1\\ 1& 5& 1\end{array}\right|=2(1-5)-3(3-1)+1(15-1)=0$
Therefore, points $(2,3),(3,1)$ and $(1,5)$ are collinear.