The using of coordinates on problem solving.
Analytic Geometry; Mathematics Teaching; Cartesian Coordinates; Problem Solving; Didactic Sequence.
The development of Analytic Geometry was a revolutionary event that profoundly transformed mathematics and, consequently, all of science, technology, and human thought. Analytic Geometry builds a bridge between Algebra and Geometry by enabling the representation of geometric properties through algebraic formulas and, consequently, allowing geometric problems to be solved using algebraic tools; and conversely, allowing algebraic equations to be visualized and understood from a geometric perspective. We also emphasize that Analytic Geometry laid the foundations for the creation of more advanced mathematical tools essential to Physics, Engineering, and Economics, such as Calculus and Linear Algebra, which have transformed our ability to construct mathematical models. In this work, we discuss the construction of coordinate systems in the plane, highlighting the natural use of Analytic Geometry in addressing problems stated in the language of Euclidean Geometry.