$\begin{array}{l}
\left\{ \begin{array}{l}
x' = \frac{x}{2}\\
y' = \frac{y}{2}
\end{array} \right. \Rightarrow M' = {V_{\left( {O,\frac{1}{2}} \right)}}\left( M \right)\\
A' = {V_{\left( {O,\frac{1}{2}} \right)}}\left( A \right) \Rightarrow \left\{ \begin{array}{l}
{x_{A'}} = \frac{1}{2}{x_A} = \frac{1}{2}.2 = 1\\
{y_{A'}} = \frac{1}{2}{y_A} = \frac{1}{2}.3 = \frac{3}{2}
\end{array} \right.\\
\Rightarrow A'\left( {1;\frac{3}{2}} \right)\\
Lay\,B\left( {0;2} \right) \in d \Rightarrow B, = {V_{\left( {O;\frac{1}{2}} \right)}}\left( B \right) \Leftrightarrow B'\left( {0;1} \right)\\
Goi\,d':x - y + c = 0\\
\Rightarrow B' \in d' \Leftrightarrow 0 - 1 + c = 0 \Leftrightarrow c = 1\\
\Rightarrow d':x - y + 1 = 0
\end{array}$
