Transformations

Transformations are a change of its point of an object on a plane. In mathematics, Transformations are of any function that replacing a set A on to a different set or on to itself. On the other hand, most often the set A has some additional algebraic or geometric structure and the term "transformation" determines a function from A to itself which protects this structure.

Types of Transformations:

 

Transformations are of three types:

  • Isometric Transformation
  • Direct Isometric Transformation.
  • Opposite Isometric Transformation.

 

Isometric Transformation:

 

A Transformation is an Isometric Transformation, if it safe guard its distance. An Isometric Transformation can be also a direct Isometric transformation or an opposite isometric Transformation.

 

Direct Isometric Transformation:

 

An Isometric transformation is said to be direct, if it safe guard its distance and direction or orientation.

 

Opposite Isometric Transformation:

 

An Isometric Transformation is opposite, if it safe guard its distance but failed to safe guard the direction or orientation.

Opposite Isometric Transformation is again classified into four types. They are:

  • Translation.
  • Rotation.
  • Reflection.
  • Glide reflection.

 Transformations-opposite Isometric Types:

 

Translation:

The process of moving object from one place to another is called Translation.  Each translation should have its direction and distance. Here the object is represented with the letter R. In translation, we can note that the position of the object that never changed.

          translatio

Rotation:

            Here the term Rotation means that the object turns it around. The every rotation has its own center and its angle of rotation.

          /rotation

Here, O represents the center point of the object.

A is the object of rotation.

 

In the Rotation, The shape and size of the object must not change but only the position of the object is changed.

 

Reflection:

 

Reflection is nothing but which create the mirror image of the object. Reflection also produces the same shape and size. It never allows the object to change its shape and size.

            reflection

Glide Reflection:

A glide reflection unites the reflection with a translation along with the direction of the mirror line. In the glide reflection, we can note that the shape of an object must not change.

            20reflection

            These are the concepts on transformations.