40319

The purple number created, by changing the quadrilateral so it has a different length and width, is calculated by how many squares the line between 0,0 and the diagonally opposite corner of the quadrilateral passes through.

e.g. if the coordinates of the opposite corner to 0,0 was 12,1 the purple number would be 12 as it only passes through 12 squares. But the coordinates were 2,3 the purple number would be 4.