$\mathrm{A}(-3,12), \mathrm{B}(7,6)$ and $C(\mathrm{x}, 9)$ are the given points. Then:

$\left(x_{1}=-3, y_{1}=12\right),\left(x_{2}=7, y_{2}=6\right) \text { and }\left(x_{3}=x, y_{3}=9\right)$

Since, that points A, B and $C$ are collinear. Therefore,

$\mathrm{x}_{1}\left(\mathrm{y}_{2}-\mathrm{y}_{3}\right)+\mathrm{x}_{2}\left(\mathrm{y}_{3}-\mathrm{y}_{1}\right)+\mathrm{x}_{3}\left(\mathrm{y}_{1}-\mathrm{y}_{2}\right)=0$

$\Rightarrow(-3)(6-9)+7(9-12)+x(12-6)=0$

$\Rightarrow(-3)(-3)+7(-3)+x(6)=0$

$\Rightarrow 9-21+6 \mathrm{x}=0$

$\Rightarrow 6 \mathrm{x}-12=0$

$\Rightarrow 6 \mathrm{x}=12$

$\Rightarrow \mathrm{x}=\frac{12}{6}=12$

Therefore, when $\mathrm{x}=2$, the given points are collinear