Math  /  Geometry

QuestionThe xyx^{\prime} y^{\prime}-coordinate system is rotated θ\theta degrees from the xyx y-coordinate system. The coordinates of a point in the xyx y-coordinate system are given. Find tt coordinates of the point in the rotated coordinate system. θ=60,(3,1)\theta=60^{\circ},(3,1)

Studdy Solution
Calculate the new coordinates:
x=32+32=3+32x' = \frac{3}{2} + \frac{\sqrt{3}}{2} = \frac{3 + \sqrt{3}}{2} y=332+12=33+12y' = -\frac{3\sqrt{3}}{2} + \frac{1}{2} = \frac{-3\sqrt{3} + 1}{2}
The coordinates of the point in the rotated xyx'y'-coordinate system are:
(3+32,33+12)\boxed{\left( \frac{3 + \sqrt{3}}{2}, \frac{-3\sqrt{3} + 1}{2} \right)}

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