Question

I have a rectangle randomly oriented with known vertices with respect to local coordinates like rows and columns as reference. distance between rows may or may not be equal to that of columns. distances are known within the rectangle are known. Also I know the coordinates of the vertices w.r.t to geographic reference frame. I wanted to compute coordinates (w.r.to geographic coordinates)of a point within the rectangle when I know the row & column numbers i.e. local coordinates. How I should do it, is there any formula we can derive for this. Appreciate any suggestion...