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

The point P (a,b) undergoes the following three transformations successively : (a) reflection about the line y = x. (b) translation through 2 units along the positive direction of x-axis. (c) rotation through angle (pi)/(4) about the origin in the anti-clockwise direction. If the co-ordinates of the final position of the point P are ( - (1)/( sqrt(2)), (7)/( sqrt(2))) , then the value of 2 a - b is equal to :

The point (4,1) undergoes the following transformations successively (i) reflection about the line y = x (ii) translation through a distance 2 units along the positive direction of y-axis . Then find the final position of the point.

The point (4,1) undergoes the following transformations successively I. Reflection about the line y =x II. Translation through a distance 2 units in the direction of positive X-axis. III. Rotation through an angle pi/4 about origin in the anticlock wise direction. Then, the final position of the point is

The point (4,1) undergoes the following transformation successively (i) Reflection about the line y=x (ii) Translation through a distance 2 unit along the positive direction (x-axis) (iii)Rotation through on angle pi//4 about origin in anticlockwise direction. Then the co-ordinates of the final points

The point (3, 2) undergoes the following transformations successively (i) Reflection with respect to the line y=x (ii) translation through 3 units along the positive direction of the X-axis (iii) Rotation through an angle of pi/6 about the origin in the clockwise direction. The final position of the point P is

The point (7,5) undergoes the following transformations successively (i) The origin is translated to (1,2). (ii) Translated through 2 units along the negative direction of the new X-axis alii) Rotated through an angle about the origin in the clockwise direction.The final position of the point (7,5) is

The point P(1,3) undergoes the following transformations successively : (i) Reflection with respect to the line y = x (ii) Translation through 3 units along the positive direction of the X-axis (iii) Rotation through an angle of (pi)/(6) about the origin in the clockwise direction. The final position of the point P is