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The acute angle $θ$ through which the coordinate axes should be rotated for the point A (2,4) to attain the new abscissa 4 is given by

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$\tan θ = 3 / 4$

$\tan θ = 5 / 6$

$\tan θ = 7 / 8$

$\tan θ = \frac{3}{2}$

answer is A.

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Detailed Solution

$(x, y) = (2, 4), X = 4$

Using $X = x \cos θ + y \sin θ$

$\Rightarrow 2 \cos θ + 4 \sin θ = 4$ dividing by sin $θ$

$\Rightarrow 2 + 4 \tan θ = 4 \sec θ$

s.b.s $∴ \tan θ = \frac{3}{4}$

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