What happens if we use Edge coords instead of edge midpoints for the new vertex coords?

Maybe that makes the midpoint /2 and the weight *2 redundant.

midpoint/2 weight*2

midpoint/2 and weight*2

midpoint/2, weight*2

midpoint/2, weight*2

midpoint/2, weight*2

midpoint/2, weight*2

midpoint/2, weight*2

midpoint/2, weight*2

midpoint/2 weight*2

midpoint/2 weight*2

How do we find the intersection point in step0?

midpoint/2 weight*2