Line L_1 of slope 2 and line L_2 of slope 1/2 intersect at the origin O. In the first quadrant, P_1, P_2, …, P_12 are 12 points on line L_1 and Q_1,…

Line $\displaystyle L_1$ of slope $\displaystyle 2$ and line $\displaystyle L_2$ of slope $\displaystyle \frac{1}{2}$ intersect at the origin $\displaystyle O$. In the first quadrant, $\displaystyle P_1$, $\displaystyle \mathrm{P}_2, \ldots, \mathrm{P}_{12}$ are $\displaystyle 12$ points on line $\displaystyle \mathrm{L}_1$ and $\displaystyle \mathrm{Q}_1, \mathrm{Q}_2, \ldots, \mathrm{Q}_9$ are $\displaystyle 9$ points on line $\displaystyle \mathrm{L}_2$. Then the total number of triangles, that can be formed having vertices at three of the $\displaystyle 22$ points $\displaystyle \mathrm{O}, \mathrm{P}_1, \mathrm{P}_2, \ldots, \mathrm{P}_{12}$, $\displaystyle \mathrm{Q}_1, \mathrm{Q}_2, \ldots, \mathrm{Q}_9$, is: