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Q.

The point (4, 1)  undergoes the following
three transformations successively. 

(i)  reflection about the line y=x

(ii)  transformation through a distance 2 units along the

positive direction of x- axis 

 (iii)   rotation through an angle p/4 about the origin in
the counter clockwise direction. Then the final position
of the point is given by the coordinates

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a

(2,72)

b

12,72

c

12,72

d

(2,72)

answer is C.

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Detailed Solution

Reflection of the point (4, 1) about the line 

y=x is  (1,4)  which is transfered to the point (3,4)  at a distance 2

units along the positive direction of x- axis 

Finally a rotation through an angle π/4 takes it to

(3cos(π/4)4sin(π/4)),(3sin(π/4)+4cos(π/4))=12,72

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