Trong hệ tọa độ \({\rm{Oxy}}\), cho \({\rm{A}}\left( {1\,;\,\,2} \right),\,\,{\rm{B}}\left( { - 2\,;\,\,3} \right)\). Tọa độ điểm I sao cho \(\overrightarrow {{\rm{IA}}} + 2\overrightarrow {{\rm{IB}}} = \vec 0\) là

Gọi \(I\left( {x\,;\,\,y} \right)\). Ta có \(\overrightarrow {{\rm{IA}}} + 2\overrightarrow {{\rm{IB}}} = \vec 0 \Leftrightarrow \left( {1 - {\rm{x}}\,;\,\,2 - {\rm{y}}} \right) + 2\left( { - 2 - {\rm{x}}\,;\,\,3 - {\rm{y}}} \right) = \left( {0\,;\,\,0} \right)\)

\( \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}{1 - x - 4 - 2x = 0}\\{2 - y + 6 - 2y = 0}\end{array} \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}{x = - 1}\\{y = \frac{8}{3}}\end{array} \Rightarrow I\left( { - 1\,;\,\,\frac{8}{3}} \right).} \right.} \right.\) Chọn C.