Finding a point dividing a segment in the harminic ratio k

### 26.16.1 Finding a point dividing a segment in the harminic ratio k

The division_point command finds a point dividing a segment is a given ratio.

- division_point takes three arguments:
  - a,b, two complex numbers or points.
  - k, a complex number.
- division_point(a,b,k) returns and draws z where (z−a)/(z−b)=k.

#### Examples

A:=point(1/2+3i/2); B:=point(2+i); D:=division_point(A,B,3+i)

affix(D)

5
2
| + |
i
2