# Four quadrants in Cartesian Plane

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.

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

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

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

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.