Transformations

Introduction Transformation in math refers to some sort of change of an object in its position or size or in both under certain condition. However, the shape of an object does not change under any transformation. Transformation of an object is normally denoted by T. When an object point X is transformed under certain condition, the image point so obtained is denoted by X’. So, T(X) = X’  X  X’ If the transformation transforms the image point X’ into the original object point X then the transformation is called the inverse transformation. Inverse transformation is denoted by T -1 If the object does not change at all i.e. the object and the image be same under a transformation, it is called identity transformation.

4 Basic Types of Transformations There are basically 4 types of transformation. Reflection, Translation, Rotation and Enlargement. Under the transformation Reflection, Translation and Rotation, the object and the image are congruent i. e. under these three transformation, the image is congruent to the object. Under such transformation, only the position of the object can be changed but not the size. Under the transformation Enlargement the object and the image may or may not be congruent. Under Enlargement, the position and the size of the object can be changed. Under Enlargement, the object and the image are similar to each other. The transformation in which the object and the image are congruent is called the congruent transformation. The transformation in which the object and the image are congruent is called the congruent transformation