The point P(1,4) occupies the positions A, B | vedclass

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(B) Reflection of point $P(1,4)$ about the line $y=x$ is $A(4,1)$.After translation of point $A(4,1)$ through a distance of $1$ unit along the positiv

Vedclass · Accepted Answer

$(2 \sqrt{2}, 3 \sqrt{2})$

Vedclass · Answer

(B) Reflection of point $P(1,4)$ about the line $y=x$ is $A(4,1)$.After translation of point $A(4,1)$ through a distance of $1$ unit along the positive direction of $X$-axis,the new coordinate is $B(5,1)$.After rotation of the point $B(5,1)$ through an angle $	heta = \frac{\pi}{4}$ about the origin in the anti-clockwise direction,the new coordinates $(x', y')$ are given by:$x' = x \cos 	heta - y \sin 	heta = 5 \cos \frac{\pi}{4} - 1 \sin \frac{\pi}{4} = \frac{5}{\sqrt{2}} - \frac{1}{\sqrt{2}} = \frac{4}{\sqrt{2}} = 2\sqrt{2}$.$y' = x \sin 	heta + y \cos 	heta = 5 \sin \frac{\pi}{4} + 1 \cos \frac{\pi}{4} = \frac{5}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \frac{6}{\sqrt{2}} = 3\sqrt{2}$.Thus,the coordinates of $C$ are $(2\sqrt{2}, 3\sqrt{2})$.Hence,option $B$ is correct.

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