If the axes are rotated by angle of $30 °,$ in anti-clockwise direction, the coordinates of point $(4, - 2 \sqrt{3})$ with respect to new axes are

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$(2, 3)$

$(\sqrt{3}, - 5)$

$(2, \sqrt{3})$

$(\sqrt{3}, 2)$

answer is B.

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Detailed Solution

$X = x \cos θ + y \sin θ = 4 (\frac{\sqrt{3}}{2}) - 2 \sqrt{3} . \frac{\sqrt{3}}{2} = \sqrt{3} Y = - x \sin θ + y \cos θ = {(- 4)}^{2} (\frac{1}{2}) - (2 \sqrt{3}) (\frac{\sqrt{3}}{2}) = - 5$

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