Question

Answer 1

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

\(\Rightarrow\overrightarrow{GM}=\left(m-3;m-4\right)\)

Mà \(\overrightarrow{AG}=2\overrightarrow{GM}\Rightarrow A\left(9-2m;10-2m\right)\)

\(\Rightarrow\overrightarrow{AN}=\left(2m-4;2m-6\right)\)

Do d' song song BC \(\Rightarrow d'\perp AM\) hay \(AN\perp GM\)

\(\Rightarrow\overrightarrow{AN}.\overrightarrow{GM}=0\Rightarrow\left(2m-4\right)\left(m-3\right)+\left(2m-6\right)\left(m-4\right)=0\)

\(\Leftrightarrow4\left(m-3\right)^2=0\Rightarrow m=3\)

\(\Rightarrow M\left(3;1\right)\Rightarrow\overrightarrow{GM}=\left(0;-1\right)=-1\left(0;1\right)\)

Phương trình BC: \(0\left(x-3\right)+1\left(y-1\right)=0\Leftrightarrow y-1=0\)