When the origin is shifted to (1, -2) by tran | vedclass

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(D) Given,origin is shifted to $(h, k) = (1, -2)$.Let the original coordinates be $(x, y) = (3, -2)$.The new coordinates $(\alpha, \beta)$ after trans

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

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(D) Given,origin is shifted to $(h, k) = (1, -2)$.Let the original coordinates be $(x, y) = (3, -2)$.The new coordinates $(\alpha, \beta)$ after translation are given by $\alpha = x - h$ and $\beta = y - k$.$\alpha = 3 - 1 = 2$ and $\beta = -2 - (-2) = 0$.So,$(\alpha, \beta) = (2, 0)$.Now,the axes are rotated about the origin by an angle $	heta = 45^{\circ}$.The new coordinates $(x', y')$ after rotation are given by:$x' = \alpha \cos 	heta + \beta \sin 	heta = 2 \cos 45^{\circ} + 0 \sin 45^{\circ} = 2 	imes \frac{1}{\sqrt{2}} = \sqrt{2}$.$y' = -\alpha \sin 	heta + \beta \cos 	heta = -2 \sin 45^{\circ} + 0 \cos 45^{\circ} = -2 	imes \frac{1}{\sqrt{2}} = -\sqrt{2}$.Thus,the transformed coordinates are $(\sqrt{2}, -\sqrt{2})$.

When the origin is shifted to $(1, -2)$ by translation of coordinate axes,the transformed coordinates of $(3, -2)$ are $(\alpha, \beta)$. If the axes are rotated about the origin through an angle of $45^{\circ}$ after the translation,then the transformed coordinates of $(\alpha, \beta)$ are

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