a, \(K\left(x_K;y_K\right)\)
Vì A là trung điểm BK nên tọa độ của A là \(\left\{{}\begin{matrix}\frac{x_K+4}{2}=2\\\frac{y_K+1}{2}=3\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x_K=0\\y_K=5\end{matrix}\right.\Rightarrow K\left(0;5\right)\)
b, \(N\left(x_N;y_N\right)\)
\(B\left(4;1\right)\) là trọng tâm \(\Delta ACN\Rightarrow\left\{{}\begin{matrix}\frac{2+5+x_N}{3}=4\\\frac{3-3+y_N}{3}=1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x_N=5\\y_K=3\end{matrix}\right.\Rightarrow K\left(5;3\right)\)
c, \(E\left(0;y_E\right)\)
\(\overrightarrow{AB}=\left(2;-2\right);\overrightarrow{EA}=\left(2;3-y_E\right)\)
Khi đó A, B, E thẳng hàng khi \(\frac{2}{2}=\frac{3-y_E}{-2}\Leftrightarrow y_E=5\)
\(\Rightarrow E\left(0;5\right)\)
