\(b,\text{PT hoành độ giao điểm: }2x-1=-x+2\\ \Leftrightarrow x=1\Leftrightarrow y=1\Leftrightarrow A\left(1;1\right)\\ c,\text{PT giao }Ox,Oy\text{ của }\left(d_2\right):\left\{{}\begin{matrix}y=0\Rightarrow x=2\Rightarrow B\left(2;0\right)\\x=0\Rightarrow y=2\Rightarrow C\left(0;2\right)\end{matrix}\right.\\ \Rightarrow S_{OBC}=\dfrac{1}{2}OB\cdot OC=\dfrac{1}{2}\left|2\right|\left|2\right|=2\left(đvdt\right)\\ d,\Leftrightarrow\left\{{}\begin{matrix}m=2\\2m\ne-1\end{matrix}\right.\Leftrightarrow m=2\\ e,\Leftrightarrow A\left(1;1\right)\in\left(d_3\right)\Leftrightarrow m+4=1\Leftrightarrow m=-3\\ f,\text{PT giao }Ox,Oy\text{ của }y=mx+2:\\ \left\{{}\begin{matrix}y=0\Rightarrow x=-\dfrac{2}{m}\Rightarrow E\left(-\dfrac{2}{m};0\right)\Rightarrow OE=\dfrac{2}{\left|m\right|}\\x=0\Rightarrow y=2\Rightarrow F\left(0;2\right)\Rightarrow OF=2\end{matrix}\right.\)
Gọi H là chân đường cao từ O đến đths \(\Leftrightarrow OH=1\)
Áp dụng HTL: \(\dfrac{1}{OH^2}=\dfrac{1}{OE^2}+\dfrac{1}{OF^2}=1\)
\(\Leftrightarrow\dfrac{m^2}{4}+\dfrac{1}{4}=1\\ \Leftrightarrow m^2+1=4\\ \Leftrightarrow m^2=3\Leftrightarrow m=\pm\sqrt{3}\)
