Gọi \(M\left(x;y\right)\) là 1 điểm thuộc (d)
\(\Rightarrow D_O\left(M\right)=M'\Leftrightarrow\left\{{}\begin{matrix}x_{M'}=2.x_O-x_M=-x_M\\y_{M'}=2y_O-y_M=-y_M\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x_M=-x_{M'}\\y_M=-y_{M'}\end{matrix}\right.\Rightarrow\left(d\right):-x_{M'}-y_{M'}-2=0\Leftrightarrow x_{M'}+y_{M'}+2=0\)
\(\Rightarrow\left(d'\right):x+y+2=0\)
\(T_{\overrightarrow{v}}\left(d'\right)=d''\Leftrightarrow T_{\overrightarrow{v}}\left(M'\right)=M''\Rightarrow\left\{{}\begin{matrix}x_{M''}=x_{M'}+a=x_{M'}+3\\y_{M''}=y_{M'}+b=y_{M'}+2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x_{M'}=x_{M''}-3\\y_{M'}=y_{M''}-2\end{matrix}\right.\Rightarrow\left(d''\right):x_{M''}-3+y_{M''}-2+2=0\)
\(\Rightarrow\left(d''\right):x+y-3=0\)
Vay dt can tim la (d''):x+y-3=0