Transsormation

 

Transformation

Transformation is a function in which every point of the geometrical figure is mapped to a unique point. By the transformation each object is transformed from one position to another position. Sometimes it changes the shape of the object also. In this case the original point or the position is called object and the point or the object after transformation is called image.  

There are four types of transformations. They are:

1.  Reflection                                3. Translation

2.  Rotation                                  4.  Enlargement or Reduction.

Isometric and non-isometric transformation

The isometric transformations are reflection, rotation and translation. They are called isometric because, in these transformations, the position of the object changes but not in shape or size.

The non–isometric transformation is the enlargement or reduction in which case the position as well as the shape or size of the object is changed after transformation. 

Combined transformation

A transformation followed by another same kind or different kind of transformation to produce a new transformation is called combination of transformation. If a transformation T₁ maps a point P to P' and another transformation T₂ maps the point P' to P", then the transformation which maps the point P to P" is called combination of transformation or the composite transformation and denoted by T₂oT₁ or T­₂T₁. The combination of transformations are reflection followed by another reflection, rotation followed by another rotation, translation followed by another translation, enlargement followed by another enlargement, reflection followed by rotation etc.