Question

Determine is the point $(1,5),(2,3),(-2,-11)$ are collinear or not.

Answer 1

The three point $A(1,5)$,$B(2,3)$ and $(-2,-11)$ are said to be collinear if area of $△ABC=0$

Area of $△ABC=\frac{1}{2}\left|\begin{array}{ccc}1& 5& 1\\ 2& 3& 1\\ -2& -11& 1\end{array}\right|$

$=\frac{1}{2}[1(3+11)-5(2+2)+1(-22+6)]$

$=\frac{1}{2}[14-20-16]=\frac{-22}{2}=-11$

Area cannot be negative ,so area of $△ABC=11$sq.units.

Hence the given points are not collinear.