Tọa độ A là:
\(\begin{cases}y=0\\ 2x+m-1=0\end{cases}\Rightarrow\begin{cases}y=0\\ 2x=-m+1\end{cases}\Rightarrow\begin{cases}y=0\\ x=\frac{-m+1}{2}\end{cases}\)
=>\(A\left(\frac{-m+1}{2};0\right)\)
=>\(OA=\sqrt{\left(\frac{-m+1}{2}-0\right)^2+\left(0-0\right)^2}=\sqrt{\left(\frac{-m+1}{2}\right)^2}=\frac{\left|m-1\right|}{2}\)
Tọa độ B là:
\(\begin{cases}x=0\\ y=2\cdot0+m-1=m-1\end{cases}\)
=>B(0;m-1)
=>\(OB=\sqrt{\left(0-0\right)^2+\left(m-1-0\right)^2}=\sqrt{\left(m-1\right)^2}=\left|m-1\right|\)
ΔOAB vuông tại O
=>\(S_{OAB}=\frac12\cdot OA\cdot OB=\frac12\cdot\frac12\cdot\left|m-1\right|\cdot\left|m-1\right|=\frac14\left(m-1\right)^2\)
\(S_{OAB}=9\)
=>\(\frac14\left(m-1\right)^2=9\)
=>\(\left(m-1\right)^2=9\cdot4=36\)
=>\(\left[\begin{array}{l}m-1=6\\ m-1=-6\end{array}\right.\Rightarrow\left[\begin{array}{l}m=6+1=7\\ m=-6+1=-5\end{array}\right.\)
