Question

For what value of $x$ are the points $(1,3),(2,2)$ and $(x,3)$ collinear?

Answer 1

Area of the triangle formed by given points

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

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

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

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

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

$\Rightarrow (x-2)=0$

$\Rightarrow x=2$

$\therefore$ the required value of $x=2$