Question

# If the axes are rotated through an angle of $$30^o$$ in the anti-clockwise direction, the coordinates of point $$(4, -2\sqrt 3)$$ with respect to new axes are

A
(2,3)
B
(3,5)
C
(2,3)
D
(3,2)

Solution

## The correct option is B $$(\sqrt 3, -5)$$The relation between coordinates $$(x,y) and (x'.y')$$ can be expressed as$$x'=x\cos\theta+y\sin\theta$$$$y'=-x\sin\theta+y\cos\theta$$$$x'=(4)\cos\,30^o+(-2\sqrt{3})\sin 30^o$$    $$=4\times\dfrac{\sqrt{3}}{2}-2\sqrt{3}\times\dfrac{1}{2}$$    $$=2\sqrt{3}-\sqrt{3}$$    $$=\sqrt{3}$$$$y'=-(4)\sin(30^o)+(-2\sqrt{3})\cos(30^o)$$$$=-4\times \dfrac{1}{2}-2\sqrt{3}\times\dfrac{\sqrt{3}}{2}$$    $$=-2+(-3)$$$$=-5$$$$\therefore$$  $$(x',y')=(\sqrt{3},-5)$$$$\therefore$$  The required co-ordinates are $$(\sqrt{3},-5)$$Maths

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