Find the coordinates of the point in the rotated coordinate system.

Question

The x'y' - coordinate system has been rotated θ degrees  from  the xy-coordinate  system.  The  coordinates of  a  point  in  the xy-coordinate  system  are  given.  Find  the coordinates of the point in the rotated coordinate system.

θ = 30^o,    (1, 3)

Answer 1

Step 1 :

The angle is and the point is .

The rotation of x - axis :

Substitute in above equation.

Substitute in above equation.

The rotation of y - axis :

Substitute in above equation.

Substitute in above equation.

Step 2 :

Multiply equation (1) by .

Add equation (1) and (3) :

Step 3 :

Substitute in equation (1).

The x'y' - co-ordinates are .

Solution :
The x'y' - co-ordinates are .