Đáp án:
\(d':\,\,\,x - 2y - 7 = 0\)
Giải thích các bước giải:
\(\begin{array}{l}
A\left( {2; - 2} \right),\,\,\,d:\,\,2x + y - 1 = 0\\
d'\,\,la\,\,anh\,\,\,cua\,\,d\,\,\,qua\,\,phep\,\,quay\,\,tam\,\,A\,\,\,goc\,\,{90^0}\\
\Rightarrow d':\,\,\,x - 2y + c = 0\\
Goi\,\,\,M'\left( {x';\,\,y'} \right)\,\,\,la\,\,anh\,\,cua\,\,\,M\left( {0;\,\,1} \right)\,\,\,quay\,\,quanh\,\,tam\,\,A\,\,goc\,\,{90^0}.\\
\Rightarrow \left\{ \begin{array}{l}
x' = \left( {x - a} \right)\cos \alpha - \left( {y - b} \right)\sin \alpha + a\\
y' = \left( {x - a} \right)\sin \alpha + \left( {y - b} \right)\cos \alpha + b
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x' = - 2\cos {90^0} - \left( {1 + 2} \right)\sin {90^0} + 2\\
y' = - 2\sin {90^0} - \left( {1 + 2} \right)\cos {90^0} - 2
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x' = - 1\\
y' = - 4
\end{array} \right. \Rightarrow M'\left( { - 1; - 4} \right)\\
M' \in d' \Rightarrow - 1 - 2.\left( { - 4} \right) + c = 0\\
\Leftrightarrow c = - 7\\
\Rightarrow d':\,\,\,x - 2y - 7 = 0.
\end{array}\)
