Difference and sum of two points in the plane

26.5.3 Difference and sum of two points in the plane

Let A and B be two points in the plane, with affixes a₁+ia₂ and b₁+ib₂ respectively.

A:=point(1+2*i):; B:=point(3+4*i):;

Then:

The difference B−A returns the affix (b₁−a₁)+i(b₂−a₂), which represents the vector AB.
vector(A,B); vector(point(0),point(B-A))
The sum B+A returns the affix (b₁+a₁)+i(b₂+a₂). If D:=point(B+A), then BD=OA.
D:=point(B+A); segment(B,D); segment(point(0),A)

Note that −A is the point symmetrical to A with respect to the origin.

The sum of three points A+B+C can be viewed as the translate of C by the vector A+B. So if A or B contains parameters, you should write this as C+(A+B) or evalc(A+B)+C.