a. Gọi \(M\left(x;y\right)\Rightarrow\left\{{}\begin{matrix}\overrightarrow{MA}=\left(-2-x;1-y\right)\\\overrightarrow{MB}=\left(3-x;-4-y\right)\end{matrix}\right.\)
\(\Rightarrow2\overrightarrow{MA}-3\overrightarrow{MB}=\left(x-13;y+14\right)\)
\(2\overrightarrow{MA}-3\overrightarrow{MB}=\overrightarrow{0}\Rightarrow\left\{{}\begin{matrix}x-13=0\\y+14=0\end{matrix}\right.\) \(\Rightarrow M\left(13;-14\right)\)
b. N đối xứng A qua B \(\Leftrightarrow B\) là trung điểm AN
\(\Rightarrow\left\{{}\begin{matrix}x_N=2x_B-x_A=8\\y_N=2y_B-y_A=-9\end{matrix}\right.\) \(\Rightarrow N\left(8;-9\right)\)
c. Do P thuộc trục hoành nên tọa độ có dạng: \(P\left(x;0\right)\) \(\Rightarrow\left\{{}\begin{matrix}\overrightarrow{AP}=\left(x+2;-1\right)\\\overrightarrow{AB}=\left(5;-5\right)\end{matrix}\right.\)
A;B;P thẳng hàng \(\Rightarrow\dfrac{x+2}{5}=\dfrac{-1}{-5}\Rightarrow x+2=1\Rightarrow x=-1\)
\(\Rightarrow P\left(-1;0\right)\)
