In this section, we will discuss about the topic Rectangular Coordinate System, which you need to study in grade IX.
Mainly there are two types of coordinate System.
1-cartesian coordinate System
2-polar coordinate System
Cartesian coordinate system:
As you can see in above figure, every point on x Axis and y axis is shown uniquely in the plane. Every point either on x axis or on y axis are at equal distance from each other. If you are given 3 Cartesian coordinate in the plane you can determine the exact position of point with the help these coordinates. Using coordinate system, geometrical things like curve can be described by Cartesian equation.
For example, a circle of radius 16 can be described in x and y coordinate can be written as x2+y2=4.
There are 3 types of dimensions
One dimension System-
In one dimension only x coordinate is there rest coordinate are 0
For example-(5, 0, 0) here dimension of x is 5 and dimension of y & z is 0
Two dimension System-
For two dimensions there are two coordinate one is in x direction and other is in y direction and z coordinate is 0.
For example – (5, 4, 0) here dimension of x is 5 ,dimension of y is 4 & dimension of z is 0.
Three dimension System-
For three-dimension all the 3 coordinate are present
(4, 5, 6)
Here dimension of x is 4, dimension of y is 5 and dimension of z is 6.
Now we will move to next coordinate system that is polar coordinate system
In this system the given points are in two dimensions and each point in the plane is determined by a distance and direction is decided by angle. The point which is fixed is called is called pole. And the ray from the pole in the fix direction is called polar axis. The distance from the pole is called radius and angle is called polar angle. The radial coordinate is given by r and the angular coordinate is given by θ or t. Angle in polar System are generally expressed as degree or radian (1 radian=360degree).
Conversion of polar coordinate to Cartesian coordinate:
The two coordinate r and θ can be converted to x and y coordinates by the following formulas X=rcosθ and y=rsinθ. (To get help on cbse sample papers click here)
In the next topic we are going to discuss Rate, distance, time, angle measures, and arc lengths and In the next session we will discuss about Isosceles triangle theorem.
Mainly there are two types of coordinate System.
1-cartesian coordinate System
2-polar coordinate System
Cartesian coordinate system:
As you can see in above figure, every point on x Axis and y axis is shown uniquely in the plane. Every point either on x axis or on y axis are at equal distance from each other. If you are given 3 Cartesian coordinate in the plane you can determine the exact position of point with the help these coordinates. Using coordinate system, geometrical things like curve can be described by Cartesian equation.
For example, a circle of radius 16 can be described in x and y coordinate can be written as x2+y2=4.
There are 3 types of dimensions
One dimension System-
In one dimension only x coordinate is there rest coordinate are 0
For example-(5, 0, 0) here dimension of x is 5 and dimension of y & z is 0
Two dimension System-
For two dimensions there are two coordinate one is in x direction and other is in y direction and z coordinate is 0.
For example – (5, 4, 0) here dimension of x is 5 ,dimension of y is 4 & dimension of z is 0.
Three dimension System-
For three-dimension all the 3 coordinate are present
(4, 5, 6)
Here dimension of x is 4, dimension of y is 5 and dimension of z is 6.
Now we will move to next coordinate system that is polar coordinate system
In this system the given points are in two dimensions and each point in the plane is determined by a distance and direction is decided by angle. The point which is fixed is called is called pole. And the ray from the pole in the fix direction is called polar axis. The distance from the pole is called radius and angle is called polar angle. The radial coordinate is given by r and the angular coordinate is given by θ or t. Angle in polar System are generally expressed as degree or radian (1 radian=360degree).
Conversion of polar coordinate to Cartesian coordinate:
The two coordinate r and θ can be converted to x and y coordinates by the following formulas X=rcosθ and y=rsinθ. (To get help on cbse sample papers click here)
In the next topic we are going to discuss Rate, distance, time, angle measures, and arc lengths and In the next session we will discuss about Isosceles triangle theorem.
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