Transformation formula for two rectangular area is really simple (assuming the same orientation of axes):
x = w/W * X;
y = h/H * Y;
where
{W,H}
are dimensions (width and height) of the source area (e.g. the smaller one).{w,h}
are the dimensions of the target area (e.g. the bigger one).{X,Y}
are the coordinates of a point in the source area space.{x,y}
are the coordinates of the same point in the target area space.
However, as Christian stated, this info is possibly pretty useless in your case.
:-)