\[\begin{array}{l}
Goi\,I\left( {x;y} \right) = AD \cap BC\\
\Rightarrow \overrightarrow {AI} = \left( {x;y - 1} \right),\overrightarrow {AB} = \left( { - 1;1} \right),\overrightarrow {CD} = \left( { - 1; - 2} \right),\overrightarrow {DI} = \left( {x;y - 3} \right)\\
I,A,B\,thang\,hang \Leftrightarrow \frac{x}{{ - 1}} = \frac{{y - 1}}{1} \Leftrightarrow x + y - 1 = 0\\
I,C,D\,thang\,hang \Leftrightarrow \frac{x}{{ - 1}} = \frac{{y - 3}}{{ - 2}} \Leftrightarrow - 2x + y - 3 = 0\\
\Rightarrow \left\{ \begin{array}{l}
x + y = 1\\
- 2x + y = 3
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = - \frac{2}{3}\\
y = \frac{5}{3}
\end{array} \right. \Rightarrow I\left( { - \frac{2}{3};\frac{5}{3}} \right)
\end{array}\]
