Đáp án: H(1;2)
Giải thích các bước giải:
$\begin{array}{l}
H\left( {x;y} \right)\\
\overrightarrow {BC} = \left( {11;2} \right);\overrightarrow {AC} = \left( {8;6} \right);\\
\overrightarrow {AH} = \left( {x - 1;y - 2} \right);\\
\overrightarrow {BH} \Rightarrow \left( {x + 2;y - 6} \right)\\
Vi\,H\,la\,truc\,tam\,\Delta ABC\\
\Rightarrow \left\{ \begin{array}{l}
AH \bot BC\\
BH \bot AC
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
\overrightarrow {AH} .\overrightarrow {BC} = 0\\
\overrightarrow {BH} .\overrightarrow {AC} = 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
11\left( {x - 1} \right) + 2\left( {y - 2} \right) = 0\\
8\left( {x + 2} \right) + 6\left( {y - 6} \right) = 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
11x + 2y = 15\\
8x + 6y = 20
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x = 1\\
y = 2
\end{array} \right. \Rightarrow H\left( {1;2} \right)
\end{array}$
