The point (4, 1) undergoes the following three transformations successively: (a) Reflection about the line y = x (b) Translation through a distance 2 units along the positive direction of the x-axis. (c) Rotation through an angle `pi/4` about the origin in the anti clockwise direction. The final position of the point is given by the co-ordinates.

The point (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 (ii) Rotation through an angle (pi)/(6) about the origin in the clockwise direction. The final position of the point P is

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 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 three successive transformations , reflection about the line y = x-1 translation through a distance 1 unit along the positive direction rotation thrpough an angle pi/4 about the origin in the anti - clockwise direction Then the coordinates of the final point are ,

The point (3,2) undergoes the following three transformations in the order given (i) Reflection bout the line y=x (ii) Translation by the distance 1 unit in the positive direction of x -axis (iii) Rotation by an angle (pi)/(4) about the origin

The point (4,1) undergoes the following two successive transformations (i) Reflection about the line y=x (ii) Translation through a distance 2 units along the positive X-axis. Then the final coordinate of the point are

The point A(4, 1) undergoes following transformations successively:reflection about line y=x translation ,through a distance of 3 units in the positive direction of x-axis(iii) rotation through an angle 105^@ in anti-clockwise direction about origin O.Then the final position of point A 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(a,b) undergoes following transformation to a new co-ordinate P'(-1/(sqrt2),7/sqrt2) (i) Reflection about y=x (ii) Translation through 2 unit in the positive direction of x-axis (iii)Rotation through an angle pi/4 in anti-clockwise sense about the origin Then the value of 2a-b is