### 26.14.5 Homothety in the plane

See Section 27.12.5 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.

#### Example

h:=homothety(i,2); h(square(1-2 i,2+i))

or:

homothety(i,2,square(1-2 i,2+i))