Bài 5:
O(0;0); A(2;1); B(-4;3): M(x;y)
=>\(\overrightarrow{OA}=\left(2;1\right);\overrightarrow{MB}=\left(-4-x;3-y\right)\)
OABM là hình bình hành
=>\(\overrightarrow{OA}=\overrightarrow{MB}\)
=>\(\left\{{}\begin{matrix}-4-x=2\\3-y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-6\\y=3-1=2\end{matrix}\right.\)
Vậy: M(-6;2)
Câu 4:
A(1;1); B(3;2); C(6;5); D(x;y)
=>\(\overrightarrow{AB}=\left(2;1\right);\overrightarrow{DC}=\left(6-x;5-y\right)\)
ABCD là hình bình hành
=>\(\overrightarrow{AB}=\overrightarrow{DC}\)
=>\(\left\{{}\begin{matrix}6-x=2\\5-y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=4\end{matrix}\right.\)
Vậy: D(4;4)
Bài 3:
\(A\left(1;1\right);B\left(-3;2\right);C\left(0;5\right);D\left(x;y\right)\)
=>\(\overrightarrow{AC}=\left(-1;4\right);\overrightarrow{BD}=\left(x+3;y-2\right)\)
\(\overrightarrow{AC}=\overrightarrow{BD}\)
=>\(\left\{{}\begin{matrix}x+3=-1\\y-2=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-4\\y=6\end{matrix}\right.\)
Vậy: D(-4;6)