a, AB: qua A(1;-2), 1 VTCP \(\overrightarrow{AB}=\left(-1;3\right)\) => VTPT: \(\left(3;1\right)\)
\(\Rightarrow AB:3\left(x-1\right)+y+2=0\Leftrightarrow3x+y-1=0\)
AC : qua A(1;-2), 1 VTCP \(\overrightarrow{AC}=\left(-3;2\right)\) => VTPT: \(\left(2;3\right)\)
\(\Rightarrow AC:2\left(x-1\right)+3\left(y+2\right)=0\)
\(\Leftrightarrow2x+3y+4=0\)
BC: qua B(0;1) , 1 VTCP \(\overrightarrow{BC}=\left(-2;-1\right)\) => VTPT: \(\left(-1;2\right)\)
\(\Rightarrow BC:-x+2y-2=0\)
b, Gọi I là trung điểm AC => \(I\left(-\frac{1}{2};-1\right)\)
Pt đg trung tuyến kẻ từ B: qua \(B\left(0;1\right)\) ; 1 VPCP \(\overrightarrow{BI}=\left(-\frac{1}{2};2\right)\)
=> VTPT: \(\left(2;\frac{1}{2}\right)\)
=> BI : \(2x+2\left(y-1\right)=0\Leftrightarrow x+y-1=0\)
c, AH: qua A(1;-2) , 1 VTPT \(\overrightarrow{BC}=\left(-2;-1\right)\)
\(\Rightarrow AH:-2\left(x-1\right)-\left(y+2\right)=0\)
\(\Leftrightarrow-2x+2-y-2=0\)
\(\Leftrightarrow-2x-y=0\)
