In this chapter we will understand the concept of quadrant graph with properties and examples.
We will also look at the types of quadrant in cartesian plane and the representation of points in different quadrants.
What is Quadrant graph ?
The plane which contains horizontal and vertical axis intersecting at point O is called quadrant graph.
⟹ horizontal line is called x axis
⟹ vertical line is called y axis
⟹ point of intersection of x & y axis is called origin
Both x & y axis are marked by numbers which help in locating the position of points.
Observe the below image.
The X axis is horizontal line shown by red color.
The Y axis is the vertical line shown by blue color.
⟹ X axis on right of origin are marked by positive number.
⟹ X axis on the left of origin are marked by negative numbers.
⟹ Y axis above the origin are marked with positive numbers.
⟹ Y axis below origin are marked with negative numbers.
Notes:
The words ” quadrant graph”, ” cartesian plane” and ” coordinate graph ” mean the same thing.
All the words are used interchangeably throughout the mathematics course. So don’t get confused with these different names.
What are Quadrants in Quadrant graph ?
The are enclosed by x and y axis in the Quadrant graph / Cartesian plane are called quadrants.
There are 4 types of quadrants in cartesian plane.
(a) 1st Quadrant ⟹ located at upper right corner of the graph. It is formed by positive x & y axis.
(b) 2nd Quadrant ⟹ located at upper left corner & formed by negative x axis and positive y axis.
(c) 3rd Quadrant ⟹ located at lower left corner of the quadrant graph. It is formed by negative x & y axis.
(d) 4th Quadrant ⟹ located at lower right corner & is formed by positive x axis and negative y axis.
Signs of different quadrant
The sign of quadrants are determined polarity of x & y axis.
Due to different polarity of axis in coordinate plane, all of the above quadrants are represented by different signs.
1st Quadrant
It is made of positive x & y axis.
Hence sign of 1st quadrant is ( + , + )
The sign tells us that any point inside the 1st quadrant has positive x & y coordinate value.
2nd Quadrant
It is made of negative x axis and positive y axis.
Hence, sign of 2nd quadrant is ( -, +)
It means that any point in 2nd quadrant will have negative x value and positive y value.
3rd Quadrant
It is made of negative x & y axis.
The sign of 3rd quadrant is ( – , – )
4th Quadrant
It is made of positive x axis and negative y axis.
The sign of 4th quadrant is ( +, – )
Note:
The number on x coordinate is also known as abscissa.
The number on y coordinate is also known as ordinate.
Plotting points on different quadrants
Here we will learn to plot & represent points in different quadrant in cartesian plane.
We will understand the concept with the help of example.
Example 01
Plot point (2, 3) in quadrant graph
Solution
x axis value ⟹ 2
y axis value ⟹ 3
Since both x & y points are positive, it means that the point lies in 1st quadrant.
Given above is the location of point (2, 3) in cartesian plane.
Method to plot location of point (2, 3) in cartesian plane.
(a) mark the point 2 on x axis and draw imaginary perpendicular line.
(b) mark the point 3 on y axis & draw imaginary perpendicular line.
(c) the point of intersection of above two imaginary line is the point (2, 3)
Example 02
Plot point (-3, -1) in quadrant graph
Solution
x axis value ⟹ -3
y axis value ⟹ -1
Since both x & y coordinates values are negative, the given point lies in 3rd quadrant.
Given below is the location of point in cartesian plane.
Example 03
Plot point (-2, 2) in cartesian plane.
Solution
x axis value ⟹ -2
y axis value ⟹ 2
Since the x value is negative and y value is positive, the point lies in 2nd quadrant.
Given below is the location of point (-2, 2) in the cartesian plane.
