Coordinate Geometry, also called Cartesian Geometry, has many mathematical applications. Let’s recall the meaning of coordinate geometry in maths. Coordinate geometry is where algebra and geometry are connected. In secondary school mathematics, most of the coordinate geometry concepts are explained in two-dimensional geometry, i.e., coordinate plane R2. Three-dimensional geometry, i.e., coordinate plane R3, can also be studied using coordinate geometry methods. In two-dimensional geometry, only the x and y-axes will be in the coordinate plane, whereas in three-dimensional geometry, the x, y and z-axes will be in the coordinate plane.
As said before, coordinate geometry is one of the most significant and exciting thoughts of mathematics. It is especially central to the maths students meeting at school. As we know, coordinate geometry connects algebra and geometry with the help of graphs of lines and curves. For example, a line’s x or y-intercept can be explained with the help of the coordinates of a point. The x and y intercepts are the points where a line intersects the x-axis and the y-axis, respectively. Thus, we can solve geometric problems algebraically and deliver geometric understandings into algebra.
There are many reasons to say that coordinate geometry is an essential technique for solving various mathematical problems. By connecting a coordinate system to the plane, we attain a new capability to judge the position. Without coordinate geometry, we could have studied only the simplest form of mathematical or geometrical shapes. Suppose there are two congruent right triangles on a plane. Without knowledge of coordinate geometry, these two right triangles can be treated as the same object. In other words, there is nothing to differentiate them. One may observe that one right triangle is clearly to the right of the other triangle. This idea of “rightness” arrives with a pointed coordinate system. Here, coordinate geometry helps get each triangle’s position and a pattern to compare their locations on the coordinate plane.
Coordinate geometry helps not only in finding the location of points, lines, figures, etc., on a plane but also helps in calculating specific parameters related to these geometrical objects. For instance, we can calculate the distance between two points, P and Q, on a plane. And this distance can be taken as a line segment on a coordinate plane with endpoints P and Q. The midpoint of this line segment can be calculated as the sum of the x-coordinates and y-coordinates and divided each of these sums by 2. Similarly, we can find the ratio at which this line segment is divided by a point or a line. Also, we can find the area of the triangle or any polygon by considering the vertices in terms of coordinate points.
Apart from the geometrical figures, we can also study vectors using coordinate geometry. Thus, coordinate geometry is the study and application of geometric figures, which includes vectors, lines, polygons, etc., on the coordinate plane. Coordinate geometry is a very adaptable and exciting form of geometry that connects to almost all other areas of mathematics, such as algebra, circles, triangles, polygons, trigonometry, etc. However, coordinate geometry is primarily employed in geometrical theories and proofs.