What is a rigid transformation?

A rigid transformation is a type of transformation in geometry that preserves the size and shape of an object. This means that the object undergoes a transformation such as translation, rotation, or reflection, but its size and shape remain the same.

Examples of rigid transformations include moving an object in a straight line without changing its size (translation), rotating an object around a fixed point (rotation), or flipping an object across a line (reflection). In each of these cases, the object is transformed in a way that maintains its original dimensions and orientation.

Rigid transformations are important in geometry and mathematics because they help us understand how objects can be moved and manipulated while still maintaining their fundamental characteristics. They are used in various applications, such as computer graphics, robotics, and engineering, to accurately represent and manipulate objects in a consistent and predictable manner.