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. **