Q.

The point (4, 1)  undergoes the followingthree transformations successively. (i)  reflection about the line y=x(ii)  transformation through a distance 2 units along thepositive direction of x- axis  (iii)   rotation through an angle p/4 about the origin inthe counter clockwise direction. Then the final positionof the point is given by the coordinates

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answer is 3.

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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 2units 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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