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The point (4,1) undergoes the following ...

The point `(4,1)` undergoes the following transformations successively
I. Reflection about the line `y =x`
II. Translation through a distance 2 units in the direction of positive X-axis.
III. Rotation through an angle `pi/4` about origin in the anticlock wise direction.
Then, the final position of the point is

A

`((7)/(sqrt2), (1)/(sqrt2))`

B

`(sqrt2, 7, sqrt2)`

C

`(-sqrt2, 7, sqrt2)`

D

`((1)/(sqrt2)-(7)/(sqrt2))`

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The correct Answer is:
A
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