What is analytical geometry?

Analytic geometry is the branch of mathematics that uses algebraic equations to describe the size and position of geometric figures on a coordinate system. Developed during the seventeenth century, it is also known as Cartesian geometry or coordinate geometry. 

(Looking for deltamath answer? Contact us today!)

Points, lines and angles are the basic figures in geometry that collectively define the shape of an object. For example, a rectangle has four vertices defined by points, four sides shown by lines and four angles equal to 90 degrees. A rhombus, parallelogram, square, kite, cube and cuboid are some of the other shapes which are also defined by points, lines and angles. 

Lines, circles and conics are some of the other geometric figures which can be described using the coordinate system in analytic geometry. A line is a continuous movement from one point to another, while a circle is a straight path around an axis. 

The x-axis and y-axis are the two primary coordinate systems in analytic geometry, both of which can be used in 2-D or 3-D. A point located at a certain distance from the origin on either axis would be written as (x,y). 

In analytic geometry, the axes converge at the origin, and the order of numbers refers to the left-hand side for x and the bottom half for y. Negative numbers represent movement toward the viewer in a horizontal plane, and positive numbers represent movement away from the viewer in a vertical plane. 

This is the type of geometry most people are familiar with from school. It is taught in secondary school algebra courses, and is usually represented by a two-dimensional plane with x and y axes, where both axes are perpendicular to each other at the origin. 

Graphs are another important geometric figure which can be studied in analytic geometry. Graphs are used in many applications such as computer graphics to place objects on the screen. They are used in social media such as Facebook and Google Maps to represent the location of each user on the network. 

A graph can be represented by a series of connected lines and their corresponding values. The first line is called the graph’s origin, and each successive line is a descendant of it. The graph can be rotated in various ways to change the direction of the lines and their values. 

It can also be changed to a different type of graph such as a lineogram. A lineogram is a graph with all the edges and nodes on the same plane, where each edge is a pair of lines that connects to each other at one or more nodes. 

The study of analytic geometry is closely related to the study of algebraic geometry, which deals with curves and surfaces defined by matrices of polynomial equations. This is because the methods and principles of both fields can be applied to solve problems in the other field, which leads to a deep relation between the two subjects.