If the axes are rotated through an angle 45°, the coordinates of (22,−32) in the new system are

(x,y)=(22,−32)θ=45°X=2212−3212=−1,Y=−2212−3212=−5 ∴(X,Y)=(−1,−5)

If the axes are rotated through an angle 45°, the coordinates of (22,−32) in the new system are

(x,y)=(22,−32)θ=45°X=2212−3212=−1,Y=−2212−3212=−5 ∴(X,Y)=(−1,−5)

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If the axes are rotated through an angle $45 °$ , the coordinates of $(2 \sqrt{2}, - 3 \sqrt{2})$ in the new system are

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$(3 \sqrt{3}, - 5)$

$(- 1, - 5)$

$(5 \sqrt{3}, - 7)$

$(7, - \sqrt{3})$

answer is B.

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$(x, y) = (2 \sqrt{2}, - 3 \sqrt{2}) θ = 45 °$

$X = 2 \sqrt{2} (\frac{1}{\sqrt{2}}) - 3 \sqrt{2} (\frac{1}{\sqrt{2}}) = - 1, Y = - 2 \sqrt{2} (\frac{1}{\sqrt{2}}) - 3 \sqrt{2} (\frac{1}{\sqrt{2}}) = - 5 ∴ (X, Y) = (- 1, - 5)$

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If the axes are rotated through an angle 45°, the coordinates of (22,−32) in the new system are

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If the axes are rotated through an angle $45 °$ , the coordinates of $(2 \sqrt{2}, - 3 \sqrt{2})$ in the new system are