Do A là giao (d) với trục tung \(\Rightarrow x_A=0\Rightarrow y_A=\left(m-2\right).0+m-1=m-1\)
\(\Rightarrow OA=\left|y_A\right|=\left|m-1\right|\)
Do B là giao (d) với trục hoành
\(\Rightarrow y_B=0\Rightarrow\left(m-2\right)x_B+m-1=0\Rightarrow x_B=-\dfrac{m-1}{m-2}\) (với \(m\ne2\))
\(\Rightarrow OB=\left|x_B\right|=\left|\dfrac{m-1}{m-2}\right|\)
\(S_{OAB}=\dfrac{1}{2}OA.OB=\dfrac{1}{2}.\left|m-1\right|.\left|\dfrac{m-1}{m-2}\right|=1\)
\(\Rightarrow\left(m-1\right)^2=2\left|m-2\right|\) (1)
TH1: \(m>2\)
(1) \(\Leftrightarrow m^2-2m+1=2m-4\Rightarrow m^2-4m+5=0\) (vô nghiệm)
TH2: \(m< 2\)
\(\left(1\right)\Leftrightarrow m^2-2m+1=2\left(2-m\right)\Leftrightarrow m^2+2m-3=0\)
\(\Rightarrow\left\{{}\begin{matrix}m=1\\m=-3\end{matrix}\right.\) (thỏa mãn)