An Angle of Rotation Is Specified, Followed by the Coordinates $x ^ { \prime } - y ^ { \prime }$

An angle of rotation is specified, followed by the coordinates of a point in the $x ^ { \prime } - y ^ { \prime }$ system. Find the coordinates of the point with respect to the $x - y$ system. $\theta = 120 ^ { \circ }$ $\left( x ^ { \prime } , y ^ { \prime } \right) = ( \sqrt { 3 } , 8 )$

A) $\left( \frac { 5 } { 2 } , \frac { 9 \sqrt { 3 } } { 2 } \right)$
B) $\left( - \frac { 9 \sqrt { 3 } } { 2 } , - \frac { 5 } { 2 } \right)$
C) $\left( - \frac { 5 } { 2 } , - \frac { 9 \sqrt { 3 } } { 2 } \right)$
D) $\left( \frac { 9 \sqrt { 3 } } { 2 } , - \frac { 5 } { 2 } \right)$
E) $\left( \frac { 9 \sqrt { 3 } } { 2 } , \frac { 5 } { 2 } \right)$

Correct Answer:

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