\(\begin{array}{l}\Delta_{1} \perp d \Rightarrow \Delta_{2} \text { có dạng } x+y+c=0, \quad I H=d\left(I, \Delta_{2}\right)=\frac{|c|}{\sqrt{2}} \\ I H=\sqrt{I M^{2}-I H^{2}}=\sqrt{4-\frac{c^{2}}{2}} \\ S_{A M N}=2 \Leftrightarrow I H \cdot M H=2 \Leftrightarrow \frac{|c|}{\sqrt{2}} \sqrt{4-\frac{c^{2}}{2}}=2 \\ \Leftrightarrow c^{4}-8 c^{2}+16=0 \Leftrightarrow\left[\begin{array}{l}c=2 \\ c=-2\end{array}\right. \\ \Rightarrow\left[\begin{array}{l}\Delta_{2}: x+y+2=0 \\ \Delta_{2}: x+y-2=0\end{array}\right. \\\end{array}\)