If the origin is shifted to `(1,-2)` and axis are rotated through an angle of `30^@` the co-ordinate of `(1,1)` in the new position are

If the origin is shifted to (h,k) and the axes are rotated through an angle theta ,then the co-ordinates of a point P(x,y) are transformed as P(X,Y)=

The co-ordinates of a point P referred to a rectangular co-ordinate system where O is the origin are (1,-2). The axes are rotated about O through an angle theta. If the co-ordinates of P in the new system are (k-1,k+1), then k^(2) is equal

(i) If the axes are rotated through an angle 30^(0) , then find the coordinates of (1,2) in the new system . (ii) If the axes are rotated through an angle 30^(0) , then find the coordinates of (-2, 4) in the new system. (iii) When the axes are rotated through an angle (pi)/(2) , find the new coordinates of the point (alpha, 0)

Origin is shifted at (1,6) and new co - ordinate of point A is (1,3) then old co - ordinates are (2,9) .

If the origin is shifted to (1,6), then the new co-ordinates of (-3,4) will be

If the origin is shifted to (5,-5) , then the new co-ordinates of (4,6) will be

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

The point (4,3) when the axes translated to the point (3,1) and then axes are rotated through 30^(@) about the origin,then the new position of the point is

If the origin is shifted to the point (2,-3) the axes remaining parallel,find the new co-ordinates of the points. (5,2)