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The line AB whose equation is x–y = 2 cuts the x-axis at A, and B is (4,2). The line segment AB is
rotated about A through an angle $\frac{π}{4}$ in anticolckwise sense. Then new position B is

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$(2, 3 \sqrt{2})$

$(2, 2 \sqrt{2})$

$(- 2, \sqrt{2})$

$(- 2, 3 \sqrt{2})$

answer is A.

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Detailed Solution

Question Image

slope of AB = 1

A = (2, 0), given B = (4, 2)

inclination of $AC = 90^{\circ}$

$A B = A C = 2 \sqrt{2}$

parametric equation

$r = 2 \sqrt{2}; C = (x_{1} + r \cos θ, y_{1} + r \sin θ)$

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