Quadrant – Definition with Examples

What Is Quadrant?

In its essence, mathematics is the study of finding relationships. From planets to atoms; abstract to detailed, mathematics helps us quantify everything. It makes us capable of understanding, analyzing, and predicting how all the known phenomena in our universe occur. And it’s not like we use some advanced level science for this, we just use … graphs. 

We graph the past and present of a phenomenon into simple figures and draw insights to predict future outcomes, and the branch of mathematics that makes this feat possible is known as Coordinate Geometry. Over the course of this article; our gameplay will be to understand the most essential elements of coordinate geometry a.k.a The Coordinate Plane and its Quadrants.

The Quadrants

In the cartesian system, the coordinate plane is divided into four equal parts by the intersection of the x-axis (the horizontal number line) and the y-axis (the vertical number line). 

the quadrants x axis and y axis

These four regions are called quadrants because they each represent one-quarter of the whole coordinate plane. They are denoted by Roman numerals and each of these quadrants have their own properties.

Quadrant I: The upper right quadrant is the first quadrant, denoted as Quadrant I. In this quadrant, the x-axis and the y-axis both have positive numbers.

Quadrant II: The upper left quadrant is the second quadrant, denoted as Quadrant II. In this quadrant, the x-axis has negative numbers and the y-axis has positive numbers.

Quadrant III: The bottom left quadrant is the third quadrant, denoted as Quadrant III. In this quadrant, both the x-axis and the y-axis have negative numbers.

Quadrant IV: The bottom right quadrant is the fourth quadrant, denoted as Quadrant IV. In this quadrant, the x-axis has positive numbers and the y-axis has negative numbers.

four regions of quadrant

Note that the quadrants follow a counterclockwise order of naming.

Locating Points on the Quadrants

The coordinate plane is called two-dimensional because anywhere on this plane where you can put your finger, the location of that point will need two things: its distance on the x-axis and its distance on the y-axis. 

The left and the bottom part of the plane have negative x-axis and negative y-axis for negative integers. The point where the number lines intersect is called the origin.

location point on the quadrants

Let’s see how the coordinate system works. We already know that any point on the coordinate plane has two aspects: distance from the x-axis and distance from the y-axis. Let’s look at this through an example. Let’s mark a random point on the plane and call it “P”.  

random (P) Point on quadrants

Now start from this point and draw a straight line on the x-axis and another straight line for the y-axis like this:

draw straight line from p point on x axis and y axis

So the location of P on the x-axis is 2 units and the location of P on the y-axis is 3 units. We denote the location of the point P as P(2,3) where (2,3) is called an ordered pair that denotes the position of P.

set location of the point P called as ordered pair

Every point on the coordinate plane is in the form of the ordered pair (x,y), where x and y are numbers that denote the position of the point with respect to the x-axis and the y-axis respectively. The origin is denoted by (0,0).

Plotting Points

Let’s say we want to plot the point A(4,-3) on the coordinate plane. 

By looking at this point, we can see that its x-coordinate is positive and y-coordinate is negative. So this point would lie in Quadrant IV.
To plot this point on the coordinate plane, we will follow these steps:

Step 1: Identify the x-coordinate of the given point. In this case, it is 4. 

Step 2: Start from the origin and move towards by 4 units on the positive x-axis.

plotting point

Step 3: The y-coordinate in (4,-3) is -3, so we will start from this new point and move this point down until it faces -3 on the negative y-axis.

plotting point  -  negative y axis

That’s all we have to do to plot a point on the coordinate plane.

Solved Examples

Example 1. Identify the quadrants in which each of the following points lie.

(i) (1,4)

(ii) (6,-3)

(iii) (-4,-4)

(iv) (-1,8)

Answer:

(i) Quadrant I, because the x-coordinate and y-coordinate are both positive.

(ii) Quadrant IV, because the x-coordinate is positive and y-coordinate is negative.

(iii) Quadrant III, because the x-coordinate and y-coordinate are both negative.

(iv) Quadrant II, because the x-coordinate is negative and y-coordinate is positive.

Example 2. Give an example of a point that lies in Quadrant III.

Answer:

 In Quadrant III, the coordinates of the x-axis and y-axis are both negative. (-1, -3) is an example of a point in this quadrant.

Example 3. What quadrant is the origin in?

Ans:

The x-axis and the y-axis intersect at the origin denoted by (0,0) since both these numbers are non-negative; the origin is said to be a part of Quadrant I.

Practice Problems

Quadrant

Attend this Quiz & Test your knowledge.

1How many quadrants are there in a cartesian plane system?

2
3
4
5
CorrectIncorrect
Correct answer is: 4
The coordinate plane is divided into four equal parts by the intersection of the x-axis and the y-axis and are called quadrants.

2The coordinate (2, 1) lies in

First Quadrant
Second Quadrant
Third Quadrant
Fourth Quadrant
CorrectIncorrect
Correct answer is: First Quadrant
First Quadrant. Both the x-coordinate and y-coordinate are positive, therefore it lies in the first quadrant.

3Which of the following points lies in the third quadrant?

(3,–5)
(6,2)
(–10,4)
(–1,–8)
CorrectIncorrect
Correct answer is: (–1,–8)
(–1,–8) since both x and y-coordinates are negative in the third quadrant.

4In the fourth quadrant, the values of x and y are

Both positive
Both negative
x is positive, y is negative
x is negative, y is positive
CorrectIncorrect
Correct answer is: x is positive, y is negative
x is positive and y is negative

Frequently Asked Questions

A quadrant is the region formed by the intersection of the x-axis and the y-axis on the coordinate plane.

The 4 quadrants are the regions formed by the intersection of the x-axis and the y-axis on the coordinate plane. Their characteristic features are given as follows:

  • Quadrant I: Both x- and y-coordinates are positive.
  • Quadrant II: The x-coordinate is negative and the y-coordinate is positive.
  • Quadrant III:  Both x- and y-coordinates are positive
  • Quadrant IV: The x-coordinate is positive and the y-coordinate is negative.

We start from the upper right quadrant and mark that as Quadrant l and move anticlockwise, marking each quadrant with Roman numerals: Quadrant ll, Quadrant lll, Quadrant IV.

The four quadrants meet at the intersection of the x- and y-axis, called the origin. The origin is denoted by (0,0).