Not sure this is a viable approach.

Start with A at (0,0) and B at (0,633).

If you put a circle with radius 257 at A and another with radius 390 at B, then C will be at the intersection of these circles. This gives two points chose one. The map will be mirrored depending on the choice. The rest of the points can be found with more circle intersections.

It can be done that way with paper and compass. Writing a program is not my problem ;-)