[tex]\it d:\ \ x+y-2=0 \Rightarrow y=2-x\ \ \ \ \ (1)\\ \\ B(x,\ y)\in d\ \stackrel{(1)}{\Longrightarrow} B(x,\ 2-x)\ \ \ \ \ \ (2)\\ \\ A(0,\ 2)\in d\\ \\ AB=2\sqrt2 \Rightarrow AB^2=8 \Rightarrow (x-0)^2+(2-x-2)^2=8 \Rightarrow x^2+x^2=8 \Rightarrow \\ \\ \Rightarrow 2x^2=8|_{:2} \Rightarrow x^2=4 \Rightarrow \sqrt{x^2}=\sqrt4 \Rightarrow |x|=2 \Rightarrow x=\pm2[/tex]
[tex]\it \ x=-2\ \stackrel{(2)}{\Longrightarrow}\ B(-2,\ 4)\\ \\ x=2\ \stackrel{(2)}{\Longrightarrow}\ B(2,\ 0)[/tex]
