The point P(3,2) undergoes the following tran | vedclass

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(B) Step $1$: Reflection of the point $P(3,2)$ about the line $y=x$ swaps the coordinates,resulting in $(2,3)$.Step $2$: Translation of $(2,3)$ by $3$

Vedclass · Accepted Answer

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

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(B) Step $1$: Reflection of the point $P(3,2)$ about the line $y=x$ swaps the coordinates,resulting in $(2,3)$.Step $2$: Translation of $(2,3)$ by $3$ units in the positive direction of the $X$-axis adds $3$ to the $x$-coordinate,resulting in $(2+3, 3) = (5,3)$.Step $3$: Rotation of the point $(x,y) = (5,3)$ through an angle $	heta = \frac{\pi}{4}$ about the origin in the counter-clockwise direction is given by the transformation:$x' = x \cos 	heta - y \sin 	heta$$y' = x \sin 	heta + y \cos 	heta$Substituting $x=5, y=3, 	heta = \frac{\pi}{4}$:$x' = 5 \left(\frac{1}{\sqrt{2}}ight) - 3 \left(\frac{1}{\sqrt{2}}ight) = \frac{2}{\sqrt{2}} = \sqrt{2}$$y' = 5 \left(\frac{1}{\sqrt{2}}ight) + 3 \left(\frac{1}{\sqrt{2}}ight) = \frac{8}{\sqrt{2}} = 4\sqrt{2}$Thus,the final position is $(\sqrt{2}, 4\sqrt{2})$. Note: The provided option $B$ in the source was $(4\sqrt{2}, -\sqrt{2})$,which corresponds to a clockwise rotation. Given the standard counter-clockwise rotation formula,the result is $(\sqrt{2}, 4\sqrt{2})$.

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