The point (4, I ) 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 the x-axis. iii. Rotation through an angle π4 about the origin in the counterclockwise direction. Then the final position of the point is given by the co ordinates

Reflection about the line y = x changes the point (4, l) to (1, 4). On the translation of (1, 4) through a distance of 2 units along the positive direction of the x-axis, the point becomes (1 + 2. 4), i.e., (3,4). On rotation about the origin through an angle π4point P takes the position P' such that OP=OP′. Also, OP=5=OP′ and cos⁡θ=3/5,sin⁡θ=4/5 . Now, x=OP′cos⁡π4+θ=5cos⁡π4cos⁡θ−sin⁡θ=5352−452=−12y=OP′sin⁡π4+θ=5sin⁡π4cos⁡θ+cos⁡π4sin⁡θ=5352+452=72P′≡−12,72