On the coordinate plane, three points $\mathrm { A } ( 3,0 ) , \mathrm { B } ( 3,3 ) , \mathrm { C } ( 0,3 )$ are mapped to $\mathrm { A } ^ { \prime } , \mathrm { B } ^ { \prime } , \mathrm { C } ^ { \prime }$ respectively by the linear transformation represented by the matrix $\left( \begin{array} { l l } k & 0 \\ 0 & k \end{array} \right) ( k > 1 )$. When the area of the common part of the interior of triangle ABC and the interior of triangle $\mathrm { A } ^ { \prime } \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime }$ is $\frac { 1 } { 2 }$, what is the value of $k$? [3 points] (1) $\frac { 3 } { 2 }$ (2) $\frac { 5 } { 3 }$ (3) $\frac { 7 } { 4 }$ (4) $\frac { 9 } { 5 }$ (5) $\frac { 11 } { 6 }$
On the coordinate plane, three points $\mathrm { A } ( 3,0 ) , \mathrm { B } ( 3,3 ) , \mathrm { C } ( 0,3 )$ are mapped to $\mathrm { A } ^ { \prime } , \mathrm { B } ^ { \prime } , \mathrm { C } ^ { \prime }$ respectively by the linear transformation represented by the matrix $\left( \begin{array} { l l } k & 0 \\ 0 & k \end{array} \right) ( k > 1 )$. When the area of the common part of the interior of triangle ABC and the interior of triangle $\mathrm { A } ^ { \prime } \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime }$ is $\frac { 1 } { 2 }$, what is the value of $k$? [3 points]\\
(1) $\frac { 3 } { 2 }$\\
(2) $\frac { 5 } { 3 }$\\
(3) $\frac { 7 } { 4 }$\\
(4) $\frac { 9 } { 5 }$\\
(5) $\frac { 11 } { 6 }$