(untitled) (Research, Society and Development, 2022)
The following article refers to obtaining the area of plane figures through the theoretical foundation of Analytical Geometry. The use of analytical geometry concepts arose from the difficulty in finding the solution proposed by plane geometry. It was noticed that the use of Cartesian axes inserted in the figure in a position in which the origin would be well determined and the sides provided would be part of the requested abscissas and ordinates, forming analytical points in the formed system. The objective of this article was to bring a strong argument in relation to the solution of the problem when thinking about the concepts of analytical geometry, favoring the speed and agility in the calculations, using the concepts of straight line, area of ​​a triangle, angle between straight lines, distance between two points, distance between point and line. The methodology proposes the solution of two problems involving the part of point and line, making the comparison with the plane geometry. As a positive result, we will have a huge application of analytical geometry in various problems of plane geometry as well as the use in everyday geometric shapes, favoring the reduction of the response time to the item in vestibular tests and public tenders.