Geometric Transformations: Reflections

This lecture covers the concept of reflections in the plane with an orthonormal coordinate system, focusing on orthogonal symmetry with respect to a given line equation. The lecture explains how to determine the image of a point under reflection, the properties of the linear part, and the significance of the constant term. Various cases are distinguished to illustrate the reflection process, leading to the derivation of the reflection formula. The lecture also discusses the conditions for a transformation to be a reflection and how to find the axis of reflection. Practical methods for identifying fixed points under reflection transformations are demonstrated, along with examples and applications.