# Quadrant – Definition, Examples, Practice Problems, FAQs

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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.

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).

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 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 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.

## 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.

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”.

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

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.

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.

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.

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

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)

(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.

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.

1

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

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

### The coordinate (2, 1) lies in

CorrectIncorrect
First Quadrant. Both the x-coordinate and y-coordinate are positive, therefore it lies in the first quadrant.
3

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

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

### In 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