### 11.15.5 Homothety in the plane: homothety

See section 12.14.5 for homotheties in space.

A homothety is a dilation about a given point. The homothety command can take two or three arguments.

If homothety has two arguments, they are a point (the center of the homothety) and a real number (the scaling ratio). homothery returns a new command which performs the dilation.
Input:

h := homothety(i, 2)

then:

h(1+i)

Output:

If homothety has three arguments, the first two arguments are a point and real number as above, and the third argument is a geometric object. homothety returns and draws the dilated object.
Input:

homothety(i, 2, 1+i)

Output:

Input:

homothety(i, 2, circle(1+i,1))

Output:

The homothety command can also take a complex number as the second argument. In that case, the result will be a rotation as well as a dilation.