If the points A(1, 2), O(0, 0) and C(a, b) are collinear, then

(c) 2a = b
The given points are A(1, 2), O(0, 0) and C(a, b).

Here, $\left(x_{1}=1, y_{1}=2\right),\left(x_{2}=0, y_{2}=0\right)$ and $\left(x_{3}=a, y_{3}=b\right)$

Points A, O and C are collinear.

$\Rightarrow x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)=0$

$\Rightarrow 1(0-b)+0(b-2)+a(2-0)=0$

$\Rightarrow-b+2 a=0$

$\Rightarrow 2 a=b$