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The coordinate axes are rotated throughan angle 135⁰. If the coordinates of a point P in the new system are known to be (4, –3) then the coordinates P in the original system are

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

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

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

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

answer is D.

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Detailed Solution

$x = X \cos θ - Y \sin θ x = 4 (\frac{- 1}{\sqrt{2}}) + 3 (\frac{1}{\sqrt{2}}) = \frac{- 1}{\sqrt{2}}; y = X \sin θ + Y \cos θ y = 4 (\frac{1}{\sqrt{2}}) - 3 (\frac{- 1}{\sqrt{2}}) = \frac{7}{\sqrt{2}}$

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