Trong mặt phẳng với hệ tọa độ Oxy, cho hình vuông ABCD có diện tích

\(A \in d:x - y - 2 = 0 \Rightarrow A\left( {t;t - 2} \right)\)

\(S = A{D^2} = 10 \Rightarrow AD = \sqrt {10} \)

\( \Rightarrow d\left( {A,CD} \right) = AD = \frac{{\left| {3t - t + 2} \right|}}{{\sqrt {10} }} = \sqrt {10} \)

\( \Leftrightarrow \left| {2t + 2} \right| = 10 \Leftrightarrow \left| {t + 1} \right| = 5 \Rightarrow \left[ {\begin{array}{*{20}{l}}{t = 4}\\{t = - 6}\end{array}} \right. \Rightarrow \left[ {\begin{array}{*{20}{l}}{A\left( {4;2} \right)}\\{A\left( { - 6; - 8} \right)}\end{array}} \right.\)

TH1: \(A\left( {4;2} \right) \Rightarrow AD\left\{ {\begin{array}{*{20}{l}}{qua{\mkern 1mu} {\mkern 1mu} A\left( {4;2} \right)}\\{ \bot CD:3x - y = 0}\end{array}} \right. \Rightarrow AD:x + 3y - 10 = 0\)

\(D = AD \cap CD \Rightarrow D:\left\{ {\begin{array}{*{20}{l}}{x + 3y - 10 = 0}\\{3x - y = 0}\end{array}} \right. \Rightarrow D\left( {1;3} \right)\)

\(C \in CD:3x - y = 0 \Rightarrow C\left( {c;3c} \right)\)

\(CD = \sqrt {10} \Rightarrow {\left( {c - 1} \right)^2} + {\left( {3c - 3} \right)^2} = 10 \Rightarrow \left[ {\begin{array}{*{20}{l}}{c = 2}\\{c = 0}\end{array}} \right. \Rightarrow \left[ {\begin{array}{*{20}{l}}{C\left( {2;6} \right)}\\{C\left( {0;0} \right)}\end{array}} \right.\)

TH2: \(A\left( { - 6; - 8} \right) \Rightarrow AD:x + 3y + 30 = 0\)

\( \Rightarrow D\left( { - 3; - 9} \right)\)

\(C\left( {c;3c} \right) \Rightarrow {\left( {c + 3} \right)^2} + {\left( {3c + 9} \right)^2} = 10 \Rightarrow \left[ {\begin{array}{*{20}{l}}{c = - 2}\\{c = - 4}\end{array}} \right. \Rightarrow \left[ {\begin{array}{*{20}{l}}{C\left( { - 2; - 6} \right)}\\{C\left( { - 4; - 12} \right)}\end{array}} \right.\).