Question

The origin of the coordinate axes is shifted to (3,4) and the axes are rotated through an angle of ${30}^{\circ }$ in the clockwise direction. Find the new coordinates of (7,-2)

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

we will do translation first and then rotation

(7,-2) becomes (7-3,-2-4) or (4,-6) after shifting the origin to (3,4)

(4-6) becomes (4 - i6) $e^{\frac{i\pi }{6}}$ after rotating the co-ordinate axes ${30}^{\circ }$ clockwise

= (4 - 6i) ($\frac{\sqrt{3}+i}{2}$)

= $\frac{4\sqrt{3}+4i-6\sqrt{3i}+6}{2}$

=$(2\sqrt{3}+3)+i(2-3\sqrt{3})$

So the coordinates are $(2\sqrt{3}+3,2-3\sqrt{3})$