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The point P(1,4) occupies the positions A, B and C respectively after under going the following three transformation successively.
I) Reflection about the line y=x.
II) Translation through a distance of 1 unit along the positive direction of X-axis.
III) Rotation of the line OB through an angle $\frac{π}{4}$ about the origoin in the anti-clockwise direction. Then, the coordinates of C are

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

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

$(\frac{5}{\sqrt{2}}, \frac{7}{\sqrt{2}})$

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

answer is B.

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Detailed Solution

A = (4,1) (After reflection)
B = (5,1) (After translation)
$C = (2 \sqrt{2}, 3 \sqrt{2})$ (After rotation)

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