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

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Question

(C) Given point is $P(3,2)$.$(i)$ Reflection of point $(3,2)$ about the line $y=x$ gives the point $(2,3)$.(ii) Translation of the point $(2,3)$ by $1

Vedclass · Accepted Answer

$(0, \sqrt{18})$

Vedclass · Answer

(C) Given point is $P(3,2)$.$(i)$ Reflection of point $(3,2)$ about the line $y=x$ gives the point $(2,3)$.(ii) Translation of the point $(2,3)$ by $1$ unit in the positive $x$-direction gives $(2+1, 3) = (3,3)$.(iii) Rotation of the point $(x,y) = (3,3)$ by an angle $	heta = \frac{\pi}{4}$ about the origin in the anti-clockwise direction is given by the transformation:$X = x \cos 	heta - y \sin 	heta = 3 \cos(\frac{\pi}{4}) - 3 \sin(\frac{\pi}{4}) = 3(\frac{1}{\sqrt{2}}) - 3(\frac{1}{\sqrt{2}}) = 0$$Y = x \sin 	heta + y \cos 	heta = 3 \sin(\frac{\pi}{4}) + 3 \cos(\frac{\pi}{4}) = 3(\frac{1}{\sqrt{2}}) + 3(\frac{1}{\sqrt{2}}) = \frac{6}{\sqrt{2}} = 3\sqrt{2} = \sqrt{18}$Thus,the final position is $(0, \sqrt{18})$.

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