What about normalized gaps?

To normalize the distance between two points in n-ary space. p0 and p1 can be n-ary vectors.
p0 = 1/2
p1 = 1/1
pdif = p1 - p0
the mid point would use the unit fraction 1/2 at:
pmid = p0 + pdif * 1/2
right?
For say a 3d vector of the above would be:
p0 = (1/2, 0, 0)
p1 = (1/1, 0, 0)
We can plot these. Say
p0 = (1/2, 1/4, 1/1)
p1 = (1/2, 1/3, -1/8)
That is a line in pure 3d space, yet the line normalization still works. The unit fraction 1/2 is half way in between p0 and p1...
pdif = p1 - p0
pmid = p0 + pdif * 1/2
Right?