# Homothety in the plane: homothety

### 13.15.5 Homothety in the plane: homothety

See Section 14.14.5 for homotheties in space.

A homothety is a dilation about a given point. The homothety command creates a homothety.

- homothety takes two mandatory arguments and one optional argument:
  - P, a point (the center of the homothety).
  - r, a number (the scaling ratio).
  - Optionally, G, a geometric object.
- homothety(P,r) returns a new command which dilates about P by a factor of r. If r is complex, this will rotate as well as scale.
- homothety(P,r,G) returns and draws the dilation of G about P by a factor or r.

#### Examples.

- Input:

  h:= homothety(i, 2)
  h(1+i)

  Output:
- Input:
  homothety(i, 2, 1+i)
  Output:
- Input:
  homothety(i, 2, circle(1+i,1))
  Output: