## Mappings of Polygons

It is possible to produce the following mappings of a polygon.

- translation by dx in direction x and by dy in direction y
- point symmetry Z
- axial symmetry (PQ)
- rotation around point Z with angle α
- homothetic stretching out of Z by factor k
- shear transformation by line PQ with angle α

At first you have to enter the coordinates of the polygon into an mask with a maximum of 14 vertices A to N.

Then you may connect the mappings.

For each of the connected mappings the image and the coordinates of the vertices are plotted.

### Example:

Counter image
A(1|1), B(5|1), C(3|5),
1. Translation: dx = 2, dy = 1
A(3|2), B(7|2), C(5|6),
2. Axial symmetry: a=(PQ), P(1/0), Q(0/1)
A(-1|-2), B(-1|-6), C(-5|-4),
3. Rotation: Z(0/0), alpha = 45°
A(0,70711|-2,1213), B(3,5355|-4,9497), C(-0,70711|-6,364),
4. Homothetic stretching: Z(0/0), k = -2
A(-1,4142|4,2426), B(-7,0711|9,8995), C(1,4142|12,728)

### See also:

Selecting the Mappings
Adjusting the Coordinate System