Reflection (Geometry)

In geometry, reflection is a geometric transformation that flips a shape across a line or plane, creating a mirror image. The original figure and its reflection are equidistant from the line (or plane) of reflection, which acts as a perpendicular bisector between corresponding points.

Reflections preserve area, angles, and distances—making them an isometry. Every point on one side of the mirror line maps to exactly one point on the other side. In 2D space, we reflect across a line; in 3D space, we reflect across a plane.

Reflections appear everywhere: in symmetry of natural forms, building design, and the behavior of light. A mirror is the physical embodiment of geometric reflection. Combining reflections creates other transformations—two reflections across parallel lines yield a translation, while two reflections across intersecting lines produce a rotation.

Reflections are foundational to group theory, crystallography, and computer graphics, where they help construct complex symmetric patterns from simple rules.

Related

Rotation (geometry), Symmetry, Transformation (geometry), Mirror, Plane (geometry), Isometry