Kẻ \(AH\perp BC\)
\(\Rightarrow S_{ABN}=\frac{1}{2}AH.BN\) ; \(S_{ANC}=\frac{1}{2}AH.NC\)
Mà \(S_{ABN}=3S_{ANC}\Rightarrow\frac{1}{2}AH.BN=\frac{3}{2}AH.NC\)
\(\Rightarrow BN=3NC\Rightarrow\overrightarrow{BN}=3\overrightarrow{NC}\)
Gọi \(N\left(a;b\right)\Rightarrow\left\{{}\begin{matrix}\overrightarrow{BN}=\left(a-2;b-3\right)\\\overrightarrow{NC}=\left(-1-a;-2-b\right)\end{matrix}\right.\)
\(\Rightarrow\left(a-2;b-3\right)=3\left(-1-a;-2-b\right)\)
\(\Rightarrow\left\{{}\begin{matrix}a-2=-3-3a\\b-3=-6-3b\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a=-\frac{1}{4}\\b=-\frac{3}{4}\end{matrix}\right.\) \(\Rightarrow N\left(-\frac{1}{4};-\frac{3}{4}\right)\)
