Question

Trong mp Oxy, Cho HBH ABCD có B(4;5) và G (0;\(\dfrac{-13}{3}\)) là trọng tâm tam giác ADc. Tìm tọa độ đỉnh D.

Answer 1

\(\overrightarrow{GB}=\left(4;\dfrac{28}{3}\right)\)

Gọi \(D\left(x;y\right)\) \(\Rightarrow\overrightarrow{DG}=\left(-x;-\dfrac{13}{3}-y\right)\)

Gọi O là tâm hbh \(\Rightarrow\left\{{}\begin{matrix}\overrightarrow{DG}=\dfrac{2}{3}\overrightarrow{DO}\\\overrightarrow{DO}=\overrightarrow{OB}\end{matrix}\right.\) 

\(\Rightarrow\overrightarrow{DG}=\dfrac{1}{3}\overrightarrow{DB}=\dfrac{1}{2}\overrightarrow{GB}\)

\(\Rightarrow\left\{{}\begin{matrix}-x=\dfrac{1}{2}.4\\-\dfrac{13}{3}-y=\dfrac{1}{2}.\dfrac{28}{3}\end{matrix}\right.\) \(\Rightarrow D\left(-2;-9\right)\)