Question

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

Answer 1

For the three points, and to be collinear we need to have area enclosed between the points equal to zero.
Here, points, and are $A\left(1,2\right),O\left(0,0\right)\mathrm{and}C\left(a,b\right)$.
$$\begin{gathered} \Rightarrow \frac{1}{2}\left|1\left(0-b\right)+0\left(b-2\right)+a\left(2-0\right)\right|=0 \\ \Rightarrow -b+2a=0 \\ \Rightarrow 2a=b \\ \Rightarrow \frac{a}{b}=\frac{1}{2} \end{gathered}$$