Answer:
Co-ordinate system is used to locate the position of a point in a plane using two perpendicular lines. Points are represented in the form of coordinates (x, y) in two-dimension with respect to x- and y- axes. In this article, we will learn about Cartesian Coordinate system.
To understand the need of coordinate system, let us consider an example, suppose Rina is a girl in your class and she sits on the 3rd column and 5th row. Then, this position can be represented as (3, 5).
Two axes – vertical axis and perpendicular axis are reference lines of a rectangular system from which distances are measured. They are obtained as follows:
Cartesian Coordinate System
Step-by-step explanation:
Take two number lines XX’ and YY’. Place XX’ in horizontal and write the numbers on it as we write in the number line. Similarly, place YY’ in vertical and proceed writing numbers on it as we write in a number line. Combine both the lines in such a way that the two lines cross each other at their zeroes or origins. The horizontal line XX’ is called the x-axis and the vertical line YY’ is called the y-axis. The point where XX’ and YY’ cross is called the origin, and is denoted by O. Since the positive numbers lie on the directions OX and OY, OX and OY are called the positive directions of the x-axis and the y-axis respectively. Similarly, OX’ and OY’ are called the negative directions of the x- and y-axes respectively.
Important Terms:
Quadrants:
Moreover, the axes divide the plane into four parts and these four parts are called quadrants (one-fourth part). Thus, we have four quadrants numbered I, II, III and IV anticlockwise from OX.
Cartesian Plane:
A plane consists of axes and quadrants. Thus, we call the plane the Cartesian Plane, or the Coordinate Plane, or the x-y plane. The axes are called the coordinate axes.
Cartesian coordinate system for one dimensional:
The Cartesian coordinate system for one dimensional space consists of a line. We choose a point O, origin on the line, a unit of length and orientation for the line. The orientation chooses which of the two half lines determined by O is the positive, and which is negative. Each point P of the line can be specified by its distance from O, taken with a negative or positive sign .
Number line:
A line with a chosen Cartesian system is called a number line. Every real number has a unique location on the line. Every point on the number line can be interpreted as a number.
