D is adjacent to either A and B, B and C, or A and C.
If D is adjacent to A and B, then it is opposite C. You can see that in this case D = C + (A-C) + (B-C) = A+B-C by drawing a picture.
Permuting the roles of A, B and C gives all possibilities.
If and are the vertices of a parallelogram, find all the possible coordinates for the point D
I managed to find one point using the fact that the vector AB is parallel to the vector CD and hence finding the vector of D. However, I cannot find the remaining two points.
Hello acevipaYes, provided we are told that the parallelogram is ABCD. However, if we're just told (as we were in your original phrasing of the question) that A, B, C and D are the vertices of a parallelogram, then the parallelogram could also be ABDC or ACBD. So there are, as has already been said, three possible positions for D.
Grandad