The origin is translated to (1,2). The point | vedclass

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Question

(C) $1$. Under the translation of the origin to $(1,2)$,the point $(7,5)$ shifts to $(7-1, 5-2) = (6,3)$.$2$. Under the translation through $2$ units

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) $1$. Under the translation of the origin to $(1,2)$,the point $(7,5)$ shifts to $(7-1, 5-2) = (6,3)$.$2$. Under the translation through $2$ units along the negative direction of the new $X$-axis,the point $(6,3)$ shifts to $(6-2, 3) = (4,3)$.$3$. Under the rotation through an angle $	heta = \frac{\pi}{4}$ in the clockwise direction,the coordinates $(x', y')$ are given by $x' = x \cos 	heta + y \sin 	heta$ and $y' = -x \sin 	heta + y \cos 	heta$.Substituting $x=4, y=3$ and $	heta = \frac{\pi}{4}$:$x' = 4 \cos \frac{\pi}{4} + 3 \sin \frac{\pi}{4} = \frac{4}{\sqrt{2}} + \frac{3}{\sqrt{2}} = \frac{7}{\sqrt{2}}$$y' = -4 \sin \frac{\pi}{4} + 3 \cos \frac{\pi}{4} = -\frac{4}{\sqrt{2}} + \frac{3}{\sqrt{2}} = -\frac{1}{\sqrt{2}}$The final position is $\left(\frac{7}{\sqrt{2}}, -\frac{1}{\sqrt{2}}ight)$.

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