Lời giải:Ta lấy điểm \(A\left( {1;1} \right) \in {\Delta _1}.\) Khi đó
\(A' = {V_{\left( {I,k} \right)}}\left( A \right) \Rightarrow \left\{ {\begin{array}{*{20}{c}}{x' = kx + \left( {1 - k} \right)a}\\{y' = ky + \left( {1 - k} \right)b}\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{x' = k + \left( {1 - k} \right)2}\\{y' = k + \left( {1 - k} \right)1}\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{x' = 2 - k}\\{y' = 1}\end{array}} \right.\)
Mà \(A' \in {\Delta _2} \Rightarrow x' - 2y' + 4 = 0 \Rightarrow 2 - k - 2.1 + 4 = 0 \Rightarrow k = 4.\)
Đáp án D
