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We'll search a link between DA, DB and DC (considered as vectors). But ABCD is a parallelogram and vectors composition says, in this case,DA+DC=DB.
So, DA-DB+DC=0 and 1+1-1 different from 0, so the point D is the center of weight for (A,1),(B,-1),(C,1).
It is important to mention that one of the most significant step in demonstrating that D is the center of weight for (A,a),(B,b),(C,c) was to prove that a+b+c different from 0.
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