While in Busselton, Australia, about 200 km south of Perth, I wondered if I was “on the opposite” side of the world. Thinking about it, I thought it was probably pretty close.
There is a great circle mapper at the following web page, which shows RDU – PER to be about 11,554 miles, which is pretty close to half way around the world. (Officially, the circumference is 24,901 at the equator and 24,959 at the poles.)
And an even better visualization of this is the following “antipodal” map. And that shows, as far as land mass, that NC is as close to opposite of south-western australia as you can get!