So you have determined where point B is? What are its coordinates?
If NBCD is a parallelogram, then N will lie on AB with the length of NB the same as the length of CD. One way to find N is to find the equation of the line through A and B, so that you have y as a function of x, use that to find the distance from a general point (x,y) on that line to B as a function of x only, set it equal to the distance from C to D and solve for x. Equivalently, treat the equation of the line through A and B and the equation of a circle with center at B, radius equal to the distance from C to D as simultaneous equations and solve for x and y.