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