If the coordinate of a point P are transformed to 4-6-3 when the axis are rotated through an angle 30- in the anti clockwise direction- then original coordinates of P are

Given: P'(X,Y)≡(4, 6√(3)), θ =30^∘ As, x=Xcosθ Ysinθ, y=Xsinθ +Ycosθ ⇒ x=4(√(3)2)+6√(3)(12), y=4(12) 6√(3)(√(3)2) ⇒ x=2√(3)+3√(3) =1, ...

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Standard XII

Mathematics

Shifting of Axes

If the coordi...

Question

If the coordinate of a point $P$ are transformed to $(4, - 6 \sqrt{3})$ when the axis are rotated through an angle $30^{\circ}$ in the anti clockwise direction, then original coordinates of $P$ are

(\sqrt{3}, 4)

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(5 \sqrt{3}, 7)

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(5 \sqrt{3}, - 7)

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(4 \sqrt{3}, - 7)

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Solution

The correct option is C $(5 \sqrt{3}, - 7)$
$(X, Y) = (4, - 6 \sqrt{3}), θ = 30^{\circ} x = X cos θ - Y sin θ = 4 (\frac{\sqrt{3}}{2}) + 6 \sqrt{3} (\frac{1}{2}) = 5 \sqrt{3} y = X sin θ + Y cos θ = 4 (\frac{1}{2}) - 6 \sqrt{3} (\frac{\sqrt{3}}{2}) = - 7$
Hence, original coordinate of $P = (5 \sqrt{3}, - 7)$

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Similar questions

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Shifting of Axes

Standard XII Mathematics

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If the coordinate of a point P are transformed to (4,−6√3) when the axis are rotated through an angle 30∘ in the anti clockwise direction, then original coordinates of P are

The correct option is C (5√3,−7) (X,Y)=(4,−6√3),θ=30∘x=Xcosθ−Ysinθ=4(√32)+6√3(12)=5√3y=Xsinθ+Ycosθ=4(12)−6√3(√32)=−7 Hence, original coordinate of P=(5√3,−7)

If the coordinate of a point $P$ are transformed to $(4, - 6 \sqrt{3})$ when the axis are rotated through an angle $30^{\circ}$ in the anti clockwise direction, then original coordinates of $P$ are