Question

Answer 1

Do M thuộc d nên tọa độ có dạng: \(M\left(2m-1;m\right)\)

\(\Rightarrow\overrightarrow{MA}=\left(2-2m;3-m\right)\) ;\(\overrightarrow{MB}=\left(-4-2m;-3-m\right)\)

\(\Rightarrow2\overrightarrow{MA}+\overrightarrow{MB}=\left(-6m;3-3m\right)\)

\(\Rightarrow\left|2\overrightarrow{MA}+\overrightarrow{MB}\right|=\sqrt{36m^2+\left(3-3m\right)^2}=\sqrt{45\left(m-\dfrac{1}{5}\right)^2+\dfrac{36}{5}}\ge\sqrt{\dfrac{36}{5}}\)

Dấu "=" xảy ra khi \(m=\dfrac{1}{5}\) hay \(M\left(-\dfrac{3}{5};\dfrac{1}{5}\right)\)