Difference and sum of two points in the plane

### 24.5.3 Difference and sum of two points in the plane

Let A and B be two points in the plane, with affixes a1+i a2 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.