Proposta de ensino de geometria analítica para o ensino médio: uma abordagem vetorial

Abstract

This paper presents a didactic-pedagogical proposal for teaching Analytical Geometry in the third year of high school, in accordance with the guidelines of the National Common Curricular Base (BNCC, 2018), focusing on the use of the vector approach as a methodological tool. Throughout the text, definitions, properties, and demonstrations that support the content covered will be explored, with special attention to conceptual precision and mathematical rigor. Among the topics covered are the study of triangles, the analysis of lines in the Cartesian plane, and the determination of intersection points, using tools that enable both the verification of alignment and parallelism and the discussion of the relative positioning of lines in the Cartesian plane. We will also present and compare two problem-solving approaches: the traditional method, based on the algebraic manipulation of Cartesian equations and coordinates, and the vector method, based on operations and properties of vectors. As an integral part of the proposal, an ebook will be presented as an educational resource, bringing together concepts, demonstrations, and solved examples to offer an accessible and structured resource for teaching and learning Analytical Geometry in high school from a vector perspective.