A transformation is an operation that moves, flips, or changes a shape to produce a new shape.
Types of transformations include translation (sliding), rotation (turning), reflection (flipping), and dilation (resizing). Rigid transformations (translation, rotation, reflection) preserve size and shape. Transformations can be represented using matrices in coordinate geometry. They are used in computer graphics, animation, robotics, and art.
Transformations were studied by Euclid in his "Elements" through the concept of congruence. Felix Klein's Erlangen Program (1872) unified geometry by studying properties preserved under different transformation groups. Matrix representations of transformations were developed in the 19th-20th centuries for computer graphics.