If the axes are rotated by an angle of 30^{ci | vedclass

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(B) Let the original coordinates be $(x, y) = (4, -2\sqrt{3})$ and the angle of rotation be $	heta = 30^{\circ}$.The transformation formulas for the

Vedclass · Accepted Answer

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

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(B) Let the original coordinates be $(x, y) = (4, -2\sqrt{3})$ and the angle of rotation be $	heta = 30^{\circ}$.The transformation formulas for the new coordinates $(X, Y)$ are given by:$X = x \cos	heta + y \sin	heta$$Y = -x \sin	heta + y \cos	heta$Substituting the values:$X = 4 \cos(30^{\circ}) + (-2\sqrt{3}) \sin(30^{\circ}) = 4(\frac{\sqrt{3}}{2}) - 2\sqrt{3}(\frac{1}{2}) = 2\sqrt{3} - \sqrt{3} = \sqrt{3}$$Y = -4 \sin(30^{\circ}) + (-2\sqrt{3}) \cos(30^{\circ}) = -4(\frac{1}{2}) - 2\sqrt{3}(\frac{\sqrt{3}}{2}) = -2 - 3 = -5$Thus,the new coordinates are $(\sqrt{3}, -5)$.

If the axes are rotated by an angle of $30^{\circ}$ in the counter-clockwise direction,find the coordinates of the point $(4, -2\sqrt{3})$ with respect to the new axes.

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