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

question 1

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.​ $\theta = 30 ^ { \circ }$ , $( 1,3 )$ ​

• A) \(\left( \frac { 3 - \sqrt { 3 } } { 2 } , \frac { 3 \sqrt { 3 } + 3 } { 2 } \right)\)
• B) \(\left( \frac { 3 - \sqrt { 3 } } { 2 } , \frac { 3 \sqrt { 3 } + 1 } { 2 } \right)\)
• C) \(\left( \frac { 3 + \sqrt { 3 } } { 2 } , \frac { 3 \sqrt { 3 } - 1 } { 2 } \right)\)
• D) \(\left( \frac { 3 + \sqrt { 3 } } { 2 } , \frac { 3 \sqrt { 3 } + 1 } { 2 } \right)\)
• E) \(\left( \frac { 3 - \sqrt { 3 } } { 2 } , \frac { 3 \sqrt { 3 } - 1 } { 2 } \right)\)

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