ANALYSIS OF THE COMPOSITION OF TWO PLANE ISOMETRIES: TRANSLATION, REFLECTION, AND ROTATION USING A LINEAR ALGEBRA APPROACH

Abstract

Geometric transformation is a branch of mathematics that focuses on the transformation (bijective function) of geometric objects in a plane or transformation in . One of the topics discussed in geometric transformation is the properties of the composition of two isometries. Generally, topics in geometric transformation are studied using an axiomatic geometry approach that requires strong geometric visualization skills.  This research aims to study the composition of two isometries through an alternative approach, specifically linear algebra.  The study focuses on deriving the properties of the composition of two isometries, namely translations, reflections, and rotations, while considering their algebraic forms.  The research methodology employed is literature study and deductive reasoning in accordance with mathematical syllogism. The results of this research are theorems that state the properties of the composition of two isometries.  Based on the findings of this study, it can be concluded that the properties of the composition of two isometries can be derived using a linear algebra approach.