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JEE MATHEMATICS MCQ: STRAIGHT LINES

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Application +4 | -1
The line x+2y=4x + 2y = 4 is translated parallel to itself by 3 units in the sense of increasing xx and then rotated by 30∘30^\circ in the clockwise direction about the point where the shifted line cuts the x-axis. The equation of the line in the new position is
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Correct option: A
y=tan⁡(θ−30∘)(x−4−35)y = \tan \left( {\theta - 30^\circ } \right)\left( {x - 4 - 3\sqrt 5 } \right)
The correct answer is A (y=tan⁡(θ−30∘)(x−4−35)y = \tan \left( {\theta - 30^\circ } \right)\left( {x - 4 - 3\sqrt 5 } \right)) because it represents the equation of the translated and rotated line, considering the shift and the clockwise rotation about the new x-intercept.

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