Uma breve introdução a transformações geométricas: isometrias e homotetia

Abstract

This work explores geometric transformations in the Cartesian plane, focusing on isometries (translation, reflection, and rotation) and homothety. To ensure a solid understanding, the work begins with a chapter on preliminary concepts. Following this, each transformation is introduced with clear definitions and practical examples designed to develop geometric reasoning. Isometries are discussed with an emphasis on their main characteristic: the preservation of the original figure's shape and size. We'll explore how they maintain distances between points and angles, resulting in a new figure that is congruent to the initial one. In contrast, homothety is detailed as a transformation focused on the enlargement and reduction of figures. It preserves the shape and proportions but alters the size, creating figures that are similar to the original. Finally, a series of exercises is provided to reinforce understanding and visualization of the concepts.