Question

For what value of $x$ are the points $(x,3),(2,2)$ and $(3,3)$ collinear?

Answer 1

Area of the triangle formed by given points

$=\frac{1}{2}|x(2-3)+2(3-3)+3(3-2)|$

$=\frac{1}{2}|-x+0+3|$

$=\frac{1}{2}|x-3|$

The given points are collinear if and only if area of triangle$=0$

$\Rightarrow \frac{1}{2}|x-3|=0$

$\Rightarrow (x-3)=0$

$\Rightarrow x=3$

$\therefore$ the required value of $x=3$