The point (4,1) undergoes the following three transformations successively.
i) Reflection about the line y=x
ii) Translation through a distance 2 units along the positive direction of x-axis
iii) Rotation through an angle $π / 4$ about the origin in the counter clockwise direction.
Then the final position of the point is given by coordinates

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$(\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}})$

$(- \sqrt{2}, 7 \sqrt{2})$

$(- \frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}})$

$(\sqrt{2}, 7 \sqrt{2})$

answer is C.

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Detailed Solution

Reflection about the line y=x, changes the point (4,1) to (1,4).
On translation of (1,4) through a distance of 2 units along positive direction of x-axis, the point becomes (1+2, 4), i.e, (3,4)
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On rotation about origin through an angle $π / 4$ the point P Also $O P = 5 = O P^{1}$ and $\cos θ = \frac{3}{5}, \sin θ = \frac{4}{5}$
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