1       2
--- x + --- y
 3       3

The screen below shows the following points as one example. Of course, one example does not prove that the formula always works.

a = (1,1)
b = (5, 3)

 1       2
--- a + --- b
 3       3

using the TI-92 instructions

[1, 1] -> a
[5, 3] -> b
Showpts({"a", "b", "(1/3)*a + (2/3)*b"}, 0,11,0,5)