1)
Ta có: $\left\{\begin{matrix}\overrightarrow{BC} = \left ( -6; -3 \right )\\ \Delta \perp BC\end{matrix}\right. \to \Delta$ có $VTPT: \overrightarrow{n} = \overrightarrow{BC} = \left ( -6; -3 \right )$
$\to PTTQ \Delta: -6.\left ( x - 1 \right ) - 3.\left ( y + 3 \right ) = 0$
$\to 2x + y + 1 = 0$
2)
Ta có: $\left\{\begin{matrix}\overrightarrow{AC} = \left ( -3; 2 \right )\\ \Delta \perp AC\end{matrix}\right. \to \Delta$ có $VTPT: \overrightarrow{n} = \overrightarrow{AC} = \left ( -3; 2 \right )$
$\to PTTQ \Delta: -3.\left ( x - 4 \right ) + 2.\left ( y - 2 \right ) = 0$
$\to 3x - 2y - 8 = 0$
3) Gọi trung điểm của $AB$ là $D$
$\to D\left ( \dfrac{5}{2}; -\dfrac{1}{2} \right )$
Ta có $\left\{\begin{matrix}\overrightarrow{AB} = \left ( 3; 5 \right )\\ \Delta_{CD} \perp AB\end{matrix}\right. \to \Delta_{CD}$ có $VTPT: \overrightarrow{n} = \overrightarrow{AB} = \left ( 3; 5 \right )$
$\to \Delta_{CD}$ có $VTPT: \overrightarrow{n_{CD}} = \left ( -\dfrac{1}{2}; \dfrac{9}{2} \right )$
$\to 3x + 5y - 5 = 0$
