Gọi H là trung điểm AB \(\Rightarrow H\left(\frac{3}{2};-1\right)\); \(\overrightarrow{AB}=\left(1;4\right)\) \(\Rightarrow AB^2=17\)
Phương trình trung trực d của AB:
\(4\left(x-\frac{3}{2}\right)-1\left(y+1\right)=0\Leftrightarrow4x-y-7=0\)
MAB đều \(\Leftrightarrow\left\{{}\begin{matrix}M\in d\\MA=AB\end{matrix}\right.\)
\(M\in d\Rightarrow M\left(x;4x-7\right)\Rightarrow\overrightarrow{AM}=\left(x-1;4x-4\right)\)
\(MA=AB\Leftrightarrow MA^2=AB^2\Leftrightarrow\left(x-1\right)^2+16\left(x-1\right)^2=17\)
\(\Leftrightarrow\left(x-1\right)^2=1\Rightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}M\left(0;-7\right)\\M\left(2;1\right)\end{matrix}\right.\)
