I là trung điểm AJ \(\Rightarrow\left\{{}\begin{matrix}x_A=2x_I-x_J=4\\y_A=2y_I-y_J=-10\end{matrix}\right.\) \(\Rightarrow A\left(4;-10\right)\)
J là trung điểm IB \(\Rightarrow\left\{{}\begin{matrix}x_B=2x_J-x_I=-5\\y_B=2y_J-y_I=11\end{matrix}\right.\) \(\Rightarrow B\left(-5;11\right)\)
a/ B là trung điểm II' \(\Rightarrow\left\{{}\begin{matrix}x_{I'}=2x_B-x_I=-11\\y_{I'}=2y_B-y_I=25\end{matrix}\right.\) \(\Rightarrow I'\left(-11;25\right)\)
b/ K là trung điểm AC \(\Rightarrow\left\{{}\begin{matrix}x_C=2x_K-x_A=\\y_C=2y_K-y_A=\end{matrix}\right.\)
Tương tự K là trung điểm BD \(\Rightarrow\left\{{}\begin{matrix}x_D=2x_K-x_B=\\y_D=2y_K-y_B=\end{matrix}\right.\)
c/ Gọi \(N\left(x;y\right)\Rightarrow\overrightarrow{MN}=\left(x-2;y-4\right)\) ; \(\overrightarrow{AB}=\left(-9;21\right)\)
Do ABMN là hình thang có 2 đáy MN=2AB
\(\Rightarrow\left[{}\begin{matrix}\overrightarrow{MN}=2\overrightarrow{AB}\\\overrightarrow{MN}=-2\overrightarrow{AB}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\left(x-2;y-4\right)=\left(-18;42\right)\\\left(x-2;y-4\right)=\left(18;-42\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}N\left(-16;46\right)\\N\left(20;-38\right)\end{matrix}\right.\)