Question

A(2;t^2) B(t;-4) C(2t;4t) D(t^2;-1). Xác định t để AB = CD

Đáp số: t=1

Answer 1

\(\overrightarrow{AB}=\left(t-2;-4-t^2\right)\) ; \(\overrightarrow{CD}=\left(t^2-2t;-1-4t\right)\)

\(\overrightarrow{AB}=\overrightarrow{CD}\Leftrightarrow\left\{{}\begin{matrix}t-2=t^2-2t\\-4-t^2=-1-4t\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}t^2-3t+2=0\\t^2-4t+3=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}t=1\\t=2\end{matrix}\right.\\\left[{}\begin{matrix}t=1\\t=3\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow t=1\)