I have two Uri objects passed into some code, one is a directory and the other is a filename (or a relative path)
var a = new Uri(\"file:///C:/Some/Dirs\");
This should do the trick for you:
var baseUri = new Uri("http://www.briankeating.net");
var absoluteUri = new Uri(baseUri, "/api/GetDefinitions");
This constructor follow the standard relative URI rules so the / are important :
http://example.net + foo = http://example.net/foohttp://example.net/foo/bar + baz = http://example.net/foo/bazhttp://example.net/foo/ + bar = http://example.net/foo/barhttp://example.net/foo + bar = http://example.net/barhttp://example.net/foo/bar/ + /baz = http://example.net/baz