Tọa độ E là nghiệm: \(\left\{{}\begin{matrix}y-2=0\\2x-y+3=0\end{matrix}\right.\) \(\Rightarrow E\left(-\dfrac{1}{2};2\right)\)
\(S_{CDE}=\dfrac{1}{2}S_{ABCD}=9\Rightarrow S_{ABCD}=18\)
\(\Rightarrow S_{ADE}=\dfrac{1}{2}AD.AE=\dfrac{1}{8}AD.AB=\dfrac{1}{8}S_{ABCD}=\dfrac{9}{4}\Rightarrow AD.AE=\dfrac{9}{2}\)
Gọi \(A\left(a;2\right)\) và \(D\left(d;2d+3\right)\Rightarrow\left\{{}\begin{matrix}\overrightarrow{EA}=\left(a+\dfrac{1}{2};0\right)\\\overrightarrow{AD}=\left(d-a;2d+1\right)\end{matrix}\right.\)
\(AB\perp AD\Rightarrow\overrightarrow{EA}.\overrightarrow{AD}=0\Rightarrow\left(a+\dfrac{1}{2}\right)\left(d-a\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}a=-\dfrac{1}{2}\left(loại\right)\\a=d\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}AE=\left|d+\dfrac{1}{2}\right|\\AD=\left|2d+1\right|\end{matrix}\right.\)
\(AE.AD=\left|\left(d+\dfrac{1}{2}\right)\left(2d+1\right)\right|=\dfrac{9}{2}\)
\(\Leftrightarrow\left(2d+1\right)^2=9\Rightarrow\left[{}\begin{matrix}d=1\left(loại\right)\\d=-2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}A\left(-2;2\right)\\D\left(-2;-1\right)\end{matrix}\right.\)
\(\overrightarrow{AB}=4\overrightarrow{AE}\Rightarrow\)tọa độ B
\(\overrightarrow{AB}=\overrightarrow{DC}\Rightarrow\) tọa độ C
