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In ancient times, math had two parts: ‘Algebra‘ and ‘Geometry.’ Algebra didn’t use shapes, and Geometry didn’t use equations. But a French mathematician named Rene Descartes brought them together. He made the Cartesian plane, which mixes algebra and geometry.
The number line is a straight line with numbers on it. Positive numbers are on the right of zero, and negative numbers are on the left. When you put two straight lines that cross each other at right angles, they create what we call coordinate axes.
Coordinate System
A Cartesian coordinate system, also known as a coordinate system, helps us find where a point is located. This point can be shown as a pair of numbers (x, y) called coordinates. The line that goes left and right is called the X-axis, and the one that goes up and down is called the Y-axis. When these two lines meet, we call that spot the origin, and we represent it with the letter ‘O’.
Note
- The coordinate plane is often referred to as the 2D plane.
- We call the horizontal line the XX’ line and the vertical line the YY’ line.
Quadrants of Coordinate System
The Cartesian plane is split into four parts by the lines XX’ and YY’, creating what we see in Figure 3:
- The area known as the first quadrant is labeled as XOY.
- The second quadrant is referred to as X’OY.
- The third quadrant is named X’OY’.
- Lastly, the fourth quadrant goes by the name Y’OX.
Also Check: Polar Coordinates
Sign Convention
We consider the ray called “OX” on the X-axis as the positive direction, while “OX'” is considered the negative direction on the X-axis. Similarly, “OY” on the Y-axis is positive, and “OY'” is negative.
So, when we measure distance along OX, it’s positive, and along OX’, it’s negative. Likewise, distance along OY is positive, and along OY’, it’s negative.
- In the first quadrant, both X and Y values are positive.
- In the second quadrant, X is negative, but Y is positive.
- In the third quadrant, both X and Y values are negative.
- In the fourth quadrant, X is positive, but Y is negative.
Cartesian Co-ordinates of Point
The X-coordinate, also known as the abscissa, of a point P is the distance of that point from the horizontal X-axis. The Y-coordinate, or ordinate, of point P is the distance from the vertical Y-axis.
So, for any point, the abscissa tells us how far it is from the X-axis, and the ordinate tells us how far it is from the Y-axis. We represent the position of a point P as (x, y).
If we pick a point on the X-axis, its distance from the X-axis is zero. Therefore, the Y-coordinate of any point on the X-axis is always zero. So, the coordinates of a point on the X-axis are written as (x, 0).
Similarly, for a point on the Y-axis, its distance from the Y-axis is zero, making the X-coordinate zero. Therefore, the coordinates of a point on the Y-axis are (0, y).
Here are a couple of important notes:
- When x is not equal to y, (x, y) is not the same as (y, x). They are only equal if x and y have the same value, meaning x = y.
- The coordinates of the origin, which is where the X-axis and Y-axis intersect, are (0, 0).
Also Check: Ordinates in Coordinate System
Types of Coordinate System
The most commonly used coordinate systems include:
- Number line
- Cartesian coordinate system
- Polar coordinate system
- Cylindrical Coordinate System and Spherical Coordinate System
Polar Coordinate System: In this coordinate system, points on a plane are represented as (r, θ). You can learn more about polar coordinates here.
Cylindrical and Spherical Coordinate System: These coordinate systems are used to describe points in three dimensions using polar coordinates, which can be written as (r, θ, Φ).
FAQs on Coordinate System
What are the 3 Coordinate Systems?
There are three commonly used coordinate systems: Cartesian, cylindrical and spherical.
What is a Coordinate System?
A coordinate system is a method for identifying the location of a point on the earth. Most coordinate systems use two numbers, a coordinate, to identify the location of a point. Each of these numbers indicates the distance between the point and some fixed reference point, called the origin.
What is XY Coordinate System called?
In the Cartesian coordinate system, the x and y coordinates are part of the x-axis and y-axis in a 2D space. For a point in space, the x and y coordinates are written as an ordered pair, (x, y). The first number represents the point's position on the x-axis, and the second number represents its position on the y-axis.
What is Cartesian Coordinate System?
The Cartesian , or rectangular , coordinate system consists of a horizontal x-axis and a vertical y-axis. The point where the axes cross is called the origin . Any point can be described as the distance it is from the origin along the x-axis and along the y-axis and is written as (x, y).
