Question 1146968
You can relocate the center back to ( 0,0 )
This operation is: ( x - 3, y - 2 ), so the paint
spot is now at ( 4 - 3, 2 - 2 ) = ( 1, 0 )
--------------------------
after rotating:
The y-value will be at:
{{{ 1*sin(theta) = sin(theta) }}}
The x-value will be at:
{{{ 1*cos(theta) = cos(theta) }}}
------------------------------------
Now you have to add ( 3,2 ) to  ( cos(theta), sin(theta) )
to put the paint spot where it should be, so
( cos(theta) + 3 , sin(theta) + 2 ) are the
new coordinates of the paint spot
----------------------------------------
Get a 2nd opinion if you need to