Finding a point dividing a segment in the harminic ratio k: division_point

### 13.17.1 Finding a point dividing a segment in the harminic ratio k: division_point

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.

- Input:
  division_point(i,2+i,3+i)
  Output:
- Input:
  affix(division_point(i,2+i,3))
  Output:

  3+i