\(\overrightarrow{AC}=\left(1;-2\right)\) ; \(\overrightarrow{BC}=\left(-2;-3\right)\)
\(C\in d\) ; \(\overrightarrow{u_d}=\left(1;1\right)\) ; \(\overrightarrow{AB}=\left(3;1\right)\Rightarrow AB\) không song song với d
\(\Rightarrow ABEC\) là hình thang khi và chỉ khi AC//BE hoặc BC//AE
Gọi \(E\left(x;x+1\right)\Rightarrow\overrightarrow{BE}=\left(x-2;x-3\right)\) ; \(\overrightarrow{AE}=\left(x+1;x-3\right)\)
\(\Rightarrow\left[{}\begin{matrix}\frac{x-2}{1}=\frac{x-3}{-2}\\\frac{x+1}{-2}=\frac{x-3}{-3}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\frac{7}{3}\\x=-9\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}E\left(\frac{7}{3};\frac{10}{3}\right)\\E\left(-9;-8\right)\end{matrix}\right.\)
