Transformation geometry
（重定向自Geometry transformation）
![A reflection against an axis followed by a reflection against a second axis parallel to the first one results in a total motion which is a translation.](/Images/godic/202501/15/Simx2=transl_OK.svg3653.png")
![A reflection against an axis followed by a reflection against a second axis not parallel to the first one results in a total motion that is a rotation around the point of intersection of the axes.](/Images/godic/202501/15/Simx2=rotOK.svg3653.png")
In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic approach to the study of geometry by focusing on groups of geometric transformations, and the properties of figures that are invariant under them. It is opposed to the classical synthetic geometry approach of Euclidean geometry, that focuses on geometric constructions.