what I'm trying to do is make the paddle follow the mouse position(red dot).
I know how to rotate the paddle relatively to the center of the screen, but I'm not sure how to determinate the coordinates.
From what I understand, you want to have the paddle be at a point on the circle nearest the mouse cursor. Here's the general way of calculating that point:
The simplest way would be to make your paddles origin at the center of the circle. Then you just need to calculate the angle and you're done (your paddle origin, or center position should be at the circle center and the paddle itself should be to the right of the circle as starting position).
Something like this:
If you want to have the paddle origin at the center of the paddle itself, then you can do the following to get a point that's always on the circle (the code to obtain the rotation will be the same as above):