The point (4, 1) undergoes the following three transformations successively I. reflection about the line y = x. II. translation through a distance of 2 units along the positive direction of X-axis. III. rotation through an angle of pi/4 about the origin in the anti-clockwise direction. The final position of the point is

Solution:

When the point (4,1) undergoes reflection, it becomes (1,4)

After translation through a distance of 2 units (1+4)+(2,0) = (3,4)

After rotation, coordinates are (√2, 7√2)

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