Hello friends, today we are going to learn about an interesting topic of mathematics known as Coordinate System. A coordinate system is a system in which we use one or more numbers to identify the position of a given point. There are different types of coordinate systems like Cartesian coordinate system, Homogeneous coordinate system, polar coordinate system, etc.
But what we have to learn are the Cartesian coordinate and the polar coordinate systems.
The Cartesian coordinate system is made with two planes or axis known as x and y Axis. Both the axes are perpendicular to each other. So both of them form two different planes. If any point lies in the Cartesian coordinate system then its position can be given by (x, y), where x and y are the distance of the point from x and y axis with respect to the origin.
In this system X is the horizontal axis in two dimensions. In this axis, points are called as the x coordinates.. Y is the vertical axis. In this axis the points are called as the y coordinates. Both these axis meet at one single point known as the Origin or the graph center.
In Cartesian coordinate system the distance between two points could also be found, like if the two given points are (x 1, y 1) and (x 2, y 2). then the distance between these two points could be found by using the formula
in this formula d = distance between the points, and the rest are known.
We can even find the equation of Line every easily in the Cartesian system, if we know the two points that lie on the line. It is done by using the two point form. If (x 1, y 1) and (x 2, y 2) are the two given points. Then the formula we will use will be
(y – y 1) = (x 2 – x 1/ y 2 – y 1) ( x – x 1)
The x, y and z axis are generally represented with i, j and k.
For Example (2, 3, 5) can be written as 2 i + 3 j + 5 k.
We write it in this form so that it becomes easy for us to solve and there is no confusion
The next one is the polar coordinate system, in this system a point is chosen as a pole and a ray from this axis is known as the polar axis.
In this coordinate system a point is represented by an angle to the ray and the distance from the pole i.e. (r, θ).
We can also convert the polar coordinates in the Cartesian form by using simple formulas. If in polar coordinates we know the angle and the ray distance, then the value of
x = r cos θ.
y = r sin θ.
So if you are comfortable with Cartesian coordinate system then you can easily find the value of x and y and then solve the problems. The conversion of one system to another is known as transformation process.
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