Gọi hoành độ M là a, do M thuộc \(\Delta\Rightarrow y_M=4-2a\Rightarrow M\left(a;4-2a\right)\)
\(\Rightarrow\overrightarrow{OM}=\left(a;4-2a\right)\) ; \(\overrightarrow{OA}=\left(1;-2\right)\)
\(\Rightarrow2\overrightarrow{OM}-\overrightarrow{OA}=2\left(a;4-2a\right)-\left(1;-2\right)=\left(2a-1;10-4a\right)\)
\(\Rightarrow\left|2\overrightarrow{OM}-\overrightarrow{OA}\right|=A=\sqrt{\left(2a-1\right)^2+\left(10-4a\right)^2}\)
\(\Rightarrow A=\sqrt{20a^2-84a+101}=\sqrt{20\left(a-\dfrac{21}{10}\right)^2+\dfrac{384}{5}}\ge\sqrt{\dfrac{384}{5}}\)
\(\Rightarrow A_{min}=\sqrt{\dfrac{384}{5}}\) khi \(a=\dfrac{21}{10}\)
\(\Rightarrow M\left(\dfrac{21}{10};\dfrac{-1}{5}\right)\)
