It’s more complicated than that. I’m assuming you’re talking about rasterizing an area (such as a triangle) rather than a line or a point. There’re quite different problems.
In the case of rasterizing an area, it initially has nothing to do with where vertex coordinates are. Initially it has everything to do with whether the center of a pixel fragment is inside the area being rasterized or not. If the center of a pixel fragment is inside the area, then the rasterizer interpolates the attributes associated with the vertices that define the area, but if it is outside, then that pixel fragment is discarded.
To do the interpolation, the actual coordinates of the vertices defining the area being rasterized are used to determine where, proportionally, the center of the pixel fragment is within that area. Those same proportions are used to interpolate between the attributes associated with the vertices defining the area.