In this chapter we will learn about 4 different types of quadrants in cartesian plane with properties and examples.
Let us first review the basics of cartesian plane.
Cartesian Plane definition
A graph with horizontal and vertical axis is known as cartesian plane.
Horizontal axis is known as X – axis and vertical axis is known as Y axis.
In cartesian plane, we can easily locate the position of given point with the help of markings on x and y axis.
For example;
Given below is the position of point P (3, 2) in cartesian plane.
The four quadrants in Cartesian Plane
The area formed by the intersection of x & y axis is called quadrant.
There are 4 quadrants formed in cartesian plane.
Given above is the image of 4 quadrants formed in the cartesian plane.
1st Quadrant
It lies in the upper right corner of the cartesian plane.
Formed by both positive x & y axis.
Examples of Ordered pairs in 1st quadrant are;
(2, 1) ⟹ x coordinate value is 1 & y coordinate value is 1
(7, 9) ⟹ x coordinate value is 7 & y coordinate value is 9
2nd Quadrant
It lies at the upper left corner of the coordinate plane.
It is formed by negative x axis and positive y axis.
Examples of ordered pair in 2nd quadrant are;
(-2, 1) ⟹ x coordinate value is -2 & y coordinate value is 1
(-3, 3) ⟹ x coordinate value is -3 & y coordinate value is 3
(-1, 6) ⟹ x coordinate value is 1 & y coordinate value is 6
3rd Quadrant
It lies at lower left corner of cartesian plane.
It is formed by negative x & y axis.
Examples of ordered pair in 3rd quadrants are;
(-2, -3) ⟹ x coordinate is -2 & y coordinate is -3
(-1, -6) ⟹ x coordinate is -1 & y coordinate is -6
(-5, -7) ⟹ x coordinate is -5 & y coordinate is -7
4th Quadrant
It lies at lower right corner of cartesian plane.
It is formed by positive x axis and negative y axis.
Examples of ordered pairs of 4th quadrants are;
(3, -6) ⟹ x coordinate is 3 & y coordinate is -6
(5, -1) ⟹ x coordinate is 5 & y coordinate is -1
(1, -2) ⟹ x coordinate is 1 & y coordinate is -2
I hope you understood the above concepts. Let us now solve some problems for further practice.
4 Quadrants of cartesian plane – solved Problems
(01) Identify the quadrants of below ordered pairs.
(a) (7, 3)
(b) (3, -3)
(c) (-2, -6)
(d) (-5, 9)
(e) (1,-4)
Solution
You can identify the quadrants on looking at the sign of x & y coordinates.
(a) (7, 3)
x coordinate ⟹ positive
y coordinate ⟹ positive
Hence, the point lies in 1st quadrant.
(b) (3, -3)
x coordinate ⟹ positive
y coordinate ⟹ negative
Hence, the point lies in 4th quadrant.
(c) (-2, -6)
x coordinate ⟹ negative
y coordinate ⟹ negative
Hence, the point lies in 3rd quadrant.
(d) (-5, 9)
x coordinate ⟹ negative
y coordinate ⟹ positive
Hence, the point lies in 2nd quadrant.
(e) (1,-4)
x coordinate ⟹ positive
y coordinate ⟹ negative
Hence, the point lies in 4th quadrant.