ДЕКАРТОВА СИСТЕМА КООРДИНАТ ЯК ІНСТРУМЕНТ ПОЗИЦІОНУВАННЯ ОБ’ЄДНАНИХ ТЕРИТОРІАЛЬНИХ ГРОМАД УКРАЇНИ

Problem statement. The need for positioning of amalgamated territorial communities (ATC) is due to their large number and lack of identification. Effective  ATC positioning requires the development of appropriate tools to take advantage of the territory. The purpose of the article is to highlight the results of using the Cartesian system of coordination of the rear positioning of ATC in the context of their sustainable development, examples of ATC Luhansk region. The research object is ATC of Luhansk region. The methods used in the reaserch are: system, comparative and graphical analysis (the Cartesian coordinate system in space). The reaserch  hypothesis  was the preparation that the Cartesian coordinate system can be used as a tool for assessing the positions of ATCs in the context of their sustainable development. Presentation of the main material: on the basis of sustainable development estimates of  ATC of Luhansk region their positions in the Cartesian coordinate system are determined with the help of geogebra software; to determine the best positions in the  ATC of Luhansk region, it is proposed to use the vector of balanced positioning; it is established that the Lozno-Oleksandrivska  ATC has the best balanced positioning.The originality and practical significance of the reaserch polarize the propositions of vicoristic Cartesian coordinate systems for the simplest tools for controlling the positions of ATC . Conclusions and prospects fot the further reaserches. For the assessment of ATC positions, it was used a middle ball of the development by three warehouse (economy, social, environmental). The result of the positioning of ATC of the Luhansk region was filled with a rosary behind an additional Cartesian coordinate system and software geogebra protection. The positions of  ATC of the Luhansk region are displayed in the areas XOZ, XYZ, XOY. For setting the best positions at the ATC of the Luhansk region, the reference station is assigned to the vector of the balanced position, which dials up, for the most unbalanced positions from the Lozno-Oleksandrivska position. Subsequent reaserches  may be directed to the value of visits for the purpose of the balanced development of ATC.