Do \(C\in CN\Rightarrow C\left(c;6\right)\)
\(M\) là trung điểm AC \(\Rightarrow\left\{{}\begin{matrix}x_M=\frac{x_A+x_C}{2}=\frac{3+c}{2}\\y_M=\frac{y_A+y_C}{2}=\frac{15}{2}\end{matrix}\right.\) \(\Rightarrow M\left(\frac{c+3}{2};\frac{15}{2}\right)\)
Do \(M\in BM\Rightarrow3\left(\frac{c+3}{2}\right)-4.\frac{15}{2}+9=0\Rightarrow c=11\Rightarrow\left\{{}\begin{matrix}C\left(11;6\right)\\M\left(7;\frac{15}{2}\right)\end{matrix}\right.\)
Tọa độ trọng tâm G là nghiệm: \(\left\{{}\begin{matrix}y-6=0\\3x-4y+9=0\end{matrix}\right.\) \(\Rightarrow G\left(5;6\right)\)
\(\overrightarrow{GB}=\frac{2}{3}\overrightarrow{MB}\Rightarrow\left(x_B-5;y_B-6\right)=\frac{2}{3}\left(x_B-7;y_B-\frac{15}{2}\right)\)
\(\Rightarrow\left\{{}\begin{matrix}x_B-5=\frac{2}{3}\left(x_B-7\right)\\y_B-6=\frac{2}{3}\left(y_B-\frac{15}{2}\right)\end{matrix}\right.\) \(\Rightarrow B\left(1;-\frac{2}{3}\right)\)
