Question

даны точки M(-4 1), N(2,-2), P(1,3) определите координаты точки О если вектор MN=вектору PO

Answer 1

$\displaystyle M(-4;1),\ \ N(2;-2),\ \ P(1;3),\ \ \overrightarrow {MN}=\overrightarrow {PO}\\\\\overrightarrow {MN}=\Big(2-(-4);-2-1\Big)=\Big(6;-3\Big)\\\\O(x_O;y_O)\\\\\overrightarrow {PO}=\Big(x_O-1;y_O-3\Big)=\Big(6;-3\Big)=\overrightarrow {MN}\\\\\left \{ {{x_O-1=6} \atop {y_O-3=-3}} \right. \ \ \ \Leftrightarrow\ \ \ \left \{ {{x_O=7} \atop {y_O=0}} \right.\ \ \ \ \ \ \ \ \ \boxed{\boldsymbol{O(7;0)}}$