a) ta có : \(\left(d_1\right)\cap\left(d_2\right)\) \(\Leftrightarrow-x+5=\dfrac{1}{4}x\Rightarrow x=4\Rightarrow y=1\)
\(\Rightarrow A\left(4;1\right)\)
ta có : \(\left(d_2\right)\cap\left(d_3\right)\) \(\Leftrightarrow4x=\dfrac{1}{4}x\Rightarrow x=0\Rightarrow y=0\)
\(\Rightarrow C\left(0;0\right)\equiv O\)
ta có \(\left(d_3\right)\cap\left(d_1\right)\) \(\Leftrightarrow-x+5=4x\Rightarrow x=1\Rightarrow y=4\)
\(\Rightarrow B\left(1;4\right)\)
vậy .................
b) ta có : \(OA=OB=\sqrt{1^2+4^2}=\sqrt{17}\)
\(\Rightarrow\Delta OAB\) là tam giác cân
c) ta có : \(AB=\sqrt{4^2+4^2}=4\sqrt{2}\)
áp dụng He-rong ta có :
\(S_{AOB}=6\sqrt{2}\)
