If the coordinates of a point P change to (2, | vedclass

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(C) Let $(x, y)$ be the original coordinates and $(X, Y)$ be the new coordinates after rotating the axes by an angle $	heta = 135^{\circ}$.The transf

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$(2 \sqrt{2}, 4 \sqrt{2})$

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(C) Let $(x, y)$ be the original coordinates and $(X, Y)$ be the new coordinates after rotating the axes by an angle $	heta = 135^{\circ}$.The transformation equations are:$x = X \cos 	heta - Y \sin 	heta$$y = X \sin 	heta + Y \cos 	heta$Given $(X, Y) = (2, -6)$ and $	heta = 135^{\circ}$:$x = 2 \cos 135^{\circ} - (-6) \sin 135^{\circ}$$y = 2 \sin 135^{\circ} + (-6) \cos 135^{\circ}$Since $\cos 135^{\circ} = -\frac{1}{\sqrt{2}}$ and $\sin 135^{\circ} = \frac{1}{\sqrt{2}}$:$x = 2 \left(-\frac{1}{\sqrt{2}}ight) + 6 \left(\frac{1}{\sqrt{2}}ight) = \frac{-2 + 6}{\sqrt{2}} = \frac{4}{\sqrt{2}} = 2 \sqrt{2}$$y = 2 \left(\frac{1}{\sqrt{2}}ight) - 6 \left(-\frac{1}{\sqrt{2}}ight) = \frac{2 + 6}{\sqrt{2}} = \frac{8}{\sqrt{2}} = 4 \sqrt{2}$Thus,the original coordinates are $(2 \sqrt{2}, 4 \sqrt{2})$.

If the coordinates of a point $P$ change to $(2, -6)$ when the coordinate axes are rotated through an angle of $135^{\circ}$,then the coordinates of $P$ in the original system are

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