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Introduction to Coordinate Geometry


Coordinate Geometry or the system of coordinate geometry has been derived from the correspondence of the points on the number line and real number. A very unique number coordinate can be represented on a number line and any of the real number can be located on the number line. The number line represents the whole of the real number. By the way of the convection the number line is a horizontal placed line at its right hand side the positive Numbers are placed and on the left hand side the negative number are placed and they both are separated by the 0 or we can say zero is placed in the middle of them.

On the vertical axis another number line is created here negative coordinates are below the horizontal line and the positive coordinates are above the horizontal line this system of representing a number line creates a Rectangular Coordinate System. Any Point on a plane is represented by two coordinates which is distance from the x-axis and the distance from the y-axis. Suppose we have a coordinate (3, 5), in this is 3 is represented on x- axis which means 3 units away from origin and 5 is represented on y- axis which means 5 units away from origin.

The introduction coordinate geometry or the coordinate system helped the mathematicians to explore Algebra and geometry. The presentation of points, lines, curve, and the various other geometric drawing and construction became easy because of coordinate geometry.

Among one of the important applications of coordinate system is the mapping of earth into latitudes and longitudes. It is believed that the first mapping of longitudes and latitudes was propounded by the “Amerigo Vespucci”.
Another practical application is in field of computers and television screen which is invention of the pixels.
This is all about introduction to coordinate geometry.

What are Coordinates?

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If we want to describe the location of a Point or body in space, then we need some parameters to show its location in space. These parameters are called as coordinates. Thus, we can say that coordinates are those quantities which are used to express the Position of a point in space. Coordinates are represented on a coordinate plane. Coordinate plane is a plane in which particle or point is located. Location of point is always described with respect to some reference. This reference is named as origin. Let's see what coordinates are in various systems.

There are three types of the coordinate systems. These are Cartesian coordinate, spherical coordinate and cylindrical coordinate systems. Other than these systems, there are rectangles or polar or oblique etc. coordinate systems. Among all these coordinate systems, Cartesian coordinate system is widely used in several applications of mathematics. Coordinates vary according to the coordinate system. There are three coordinates defined in the Cartesian, spherical and cylindrical coordinate system. In Cartesian coordinate system, three coordinates are ‘x’, ’y’, and ’z’. These can be figured out as shown below:

If an object or point is placed in 2 – D space then only 'x' and y- coordinates of Cartesian coordinate system are used and for 3 – D space, all three coordinates that is x, y and z coordinates are used. Coordinates on x – axis, y – axis and z – axis are called as x, y and z – coordinates respectively. If a point is located in two dimensional space at (5, 6), it indicates that point has location 5 units horizontally and 6 units vertically.

In spherical coordinate system, three coordinates are radial distance (ρ), polar angle (θ) and the azimuth angle (φ) which describes the particle in spherical Coordinate Plane. Three coordinates in cylindrical coordinate system are radial distance (ρ), the azimuth angle (φ) and z coordinate similar to Cartesian coordinate.