Question

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

(I) Reflection about the line y = x

(II) Transformation through a distance 2 unit along the positive direction of x-axis.

(III) Rotation through an angle π/4 about the origin in the a counter clockwise direction.

Then, the final position of the point is given by the coordinates

Answer 1

Correct option: (c)

Explanation:

Let B, C, D be the position of the point A (4,1) after the three operations I, II and III respectively. Then, A is ( 1, 4), C(1+ 2,4) i.e, (3,4). The point D is obtained from C by rotating the coordinate axes through an angle π/4 in anticlockwise direction.

Therefore, the coordinates of D are given by