A transformation is a general term for four specific ways to manipulate the shape of a point, a line, or shape.
The original shape of the object is called the preimage and the final shape and position of the object is the image under the transformation.

Types of transformations in math
 Translation
 Reflection
 Rotation
 Dilation
A compositions of transformations means that two or more transformations will be performed on one object. For instance, we could perform a reflection and then a translation on the same point.
There are several interesting theorems involving the composition of reflections.
Important Terms & Definitions
 Preimage: the figure prior to the transformation.
 Image: The figure after the transformation.
 Isometry: a transformation that preserves congruence. In other words, a transformation in which the image and preimage have the same side lengths and angle measurements. The following transformations maintain their mathematical congruence.
 Translations (a translation is considered a 'direct isometry' because it not only maintains congruence, but it also, unlike reflections and rotations, preserves its orientation.
 Rotations
 Reflections
 Dilations
 On the other hand,a dilation is not an isometry because its image is not congruent with its preimage.