A point (1, 1) undergoes reflection in the x-axis and then the coordinates axes are rotated through an angle of `pi/4` in anticlockwise direction. The final position of the point in the new coordinate system is

A point (2,2) undergoes reflection in the x . axis and then the coordinate axe are rotated through an angle of (pi)/(4) in anticlockwise direction.The final position of the point in the new coordinate system is

If origin is shifted to the point (2,3) and the axes are rotated through an angle pi//4 in the anticlokwise direction, then find the coordinates of the point (7, 11) in the new system of coordinates.

If the axes are rotated through an angle of 45^(@) in the clockwise direction, the coordinates of a point in the new systeme are (0,-2) then its original coordinates are

If the axes are rotated through an angle of 30^(@) in the clockwise direction, the point (4,-2 sqrt3) in the new system was formerly

If the axes are rotated through 60^@ in anticlockwise direction about origin. Find co-ordinates of point(2,6) in new co-ordinate axes.

The line 2x-y=3 is rotated through an angle (pi)/(4) in anticlockwise direction about the point (2,1) ,then equation of line in its new position

If the axes are rotated through an angle of 30^(@) in the anti clockwise direction,then coordinates of point (4,-2sqrt(3)) with respect to new axes are

When axes are rotated through an angle of 45^(@) in positive direction without changing origin then the coordinates of (sqrt(2),4) in old system are

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.

Keeping the origin constant axes are rotated at an angle 30^@ in anticlockwise direction then new coordinate of (2, 1) with respect to old axes is