Line L_1 of slope 2 and line L_2 of slope (1)/(2) intersect at the origin O .

Question

Line $L_1$ of slope 2 and line $L_2$ of slope $\frac{1}{2}$ intersect at the origin O . In the first quadrant, $\mathrm{P}_1$, $P_2, \ldots, P_{12}$ are 12 points on line $L_1$ and $Q_1, Q_2, \ldots, Q_9$ are 9 points on line $L_2$. Then th...

Accepted Answer

Total triangles

(2 points as $y=\frac{x}{2},1$ point on $y=\frac{x}{2}$)

$+2($ points and $y=\frac{x}{2},1$ point on $y=2x$)

+(1 point on $y=2x,1)$ point on $y=\frac{x}{2}$ and origin)

$={}^{9}{C}_{2},{}^{12}{C}_{1}+{}^{9}{C}_{1}{}^{12}{C}_{2}+{}^{9}{C}_{1}\cdot {}^{12}{C}_{1}\cdot {}^{1}{C}_{1}$

$=1134$

Solutions · 1