The $x ^ { \prime } y ^ { \prime }$

Multiple Choice

The $x ^ { \prime } y ^ { \prime }$ -coordinate system has been rotated $\theta$ degrees from the $x y$ -coordinate system.The coordinates of a point in the $x y$ -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. $\theta = 45 ^ { \circ }$ , $( 9,2 )$

A) $\left( \frac { 11 \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right)$
B) $\left( - \frac { 11 \sqrt { 2 } } { 2 } , - \frac { 7 \sqrt { 2 } } { 2 } \right)$
C) $\left( \frac { 11 } { 2 } , - \frac { 7 \sqrt { 2 } } { 2 } \right)$
D) $\left( \frac { 11 \sqrt { 2 } } { 2 } , \frac { 7 \sqrt { 2 } } { 2 } \right)$
E) $\left( \frac { 11 \sqrt { 2 } } { 2 } , - \frac { 7 \sqrt { 2 } } { 2 } \right)$