The point (4, 1) undergoes the following thre | vedclass

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(C) Step $1$: Reflection of $(4, 1)$ about the line $y = x$ gives the point $(1, 4)$.Step $2$: Translation of $(1, 4)$ by $2$ units along the positive

Vedclass · Accepted Answer

$\left( -\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}} \right)$

Vedclass · Answer

(C) Step $1$: Reflection of $(4, 1)$ about the line $y = x$ gives the point $(1, 4)$.Step $2$: Translation of $(1, 4)$ by $2$ units along the positive $x$-axis gives $(1 + 2, 4) = (3, 4)$.Step $3$: Rotation of $(3, 4)$ through an angle $	heta = \pi/4$ about the origin in the anti-clockwise direction is given by the transformation:$x' = x \cos 	heta - y \sin 	heta = 3 \cos(\pi/4) - 4 \sin(\pi/4) = 3(1/\sqrt{2}) - 4(1/\sqrt{2}) = -1/\sqrt{2}$$y' = x \sin 	heta + y \cos 	heta = 3 \sin(\pi/4) + 4 \cos(\pi/4) = 3(1/\sqrt{2}) + 4(1/\sqrt{2}) = 7/\sqrt{2}$Thus,the final position is $\left( -\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}} ight)$.

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