What is a rigid motion?

A rigid motion, also known as an isometry, is a type of transformation that preserves the distance between points in a geometric figure. This means that the shape and size of the figure remain constant after undergoing a rigid motion.

There are three main types of rigid motions: translations, rotations, and reflections.

• Translations involve moving a figure in a specific direction without changing its orientation or shape. The figure is shifted by a certain distance in a specified direction.

• Rotations involve rotating a figure around a fixed point, called the center of rotation. The figure is turned by a certain angle in a specified direction.

• Reflections involve flipping a figure over a line, called the line of reflection. The figure is mirrored across the line, creating a mirror image of the original figure.

Rigid motions are often used in geometry to study the properties of geometric figures and to prove geometric theorems. They are important tools in understanding the relationships between shapes and patterns in mathematics.