M(-11/5; 3)
N(0; 0)
a/ \(\Rightarrow\left(x_A-x_M;y_A-y_M\right)=2\left(x_B-x_M;y_B-y_M\right)+4\left(x_C-x_M;y_C-y_M\right)\)
\(\Leftrightarrow\left(5-x_M;9-y_M\right)=2\left(1-x_M;6-y_M\right)+4\left(-2-x_M;3-y_M\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}5-x_M=2-2x_M-8-4x_M\\9-y_M=12-2y_M+12-4y_M\end{matrix}\right.\)
Tự gioải nốt nhoè :)
b/ \(\left\{{}\begin{matrix}N\in Oy\\N\in BC\end{matrix}\right.\)
ptđt đi qua B và C: \(\left\{{}\begin{matrix}a+b=6\\-2a+b=3\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a=1\\b=5\end{matrix}\right.\)
\(\Rightarrow y=x+5\)
Có y=0 => x= -5
\(\Rightarrow N\left(-5;0\right)\)
