Umbilical cord DNA

If a DNA test is run on a sample of a human umbilical cord, will it match the mother or the child?

My guess would be the child, since the umbilical cord is axually a part of the fetus, and never really connected to the mother, except through the placenta (as I understand it, being neither a woman nor a doctor).

When a fertilized egg implants (and this goes for all the placental mammals), it quickly divides into two parts. One becomes the embryo. The other begins forming the placenta, from which the umbilical cord grows. So if you take a sample from the placenta or umbilical cord after the birth, and check the DNA, you will be looking at the baby’s DNA, not his mother’s.

That was pretty much my guess, too, but once I started to think about the question I had to admit that I wasn’t absolutely sure. Thanks to you both.