[tex]\it AB^2=(x_B-x_A)^2+(y_B-y_A)^2=(7-2a)^2+(2a+2-9)^2=\\ \\ =(7-2a)^2+(7+2a)^2=49-28a+4a^2+49+28a+4a^2=8a^2+98\ \ \ \ \ \(1)\\ \\ AB=\sqrt{162}\ \Rightarrow AB^2=162\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow 8a^2+98=162\Big|_{-98} \Rightarrow 8a^2=64|_{:8} \Rightarrow a^2=8 \Rightarrow \\ \\ \Rightarrow \sqrt{a^2}=\sqrt8 \Rightarrow |a|=\sqrt{4\cdot2} \Rightarrow a=\pm2\sqrt2[/tex]
