Quadrants on a Cartesian Plane

The four quadrants on a cartesian plane are created by the intersection of X and Y-axes. A quadrant is defined as the area enclosed by the intersection of the x and y axis. Each quadrant on a Cartesian plane has either positive or negative value of x, y coordinates based on the quadrant it is located in. These two values are called the coordinates of a point. On this page, we will learn more about four quadrants on a cartesian plane and its relation with the value of coordinates of a point. Let’s start with understanding what are the coordinates of a point on a cartesian plane and how they are located in each quadrant.

Table of Contents

• Coordinates of a Point on a Cartesian Plane
• Four Quadrants of a Cartesian Plane
• How to Plot Points on a Cartesian Plane
• Solved Examples on Quadrants of a Cartesian Plane

Coordinates of a Point on a Cartesian Plane

A cartesian plane also known as a coordinate plane can be defined as a plane formed by intersection of two perpendicular lines called the axes of a plane. The horizontal axis is called the x-axis and the vertical axis is called the y-axis. The point at which both these lines intersect is called the origin ‘O’ represented through coordinates O(0,0) and the lines divide the plane into four parts called the quadrants of a plane. So, the plane consists of the axes and these quadrants. Any point of a cartesian plane is represented by its x and y coordinates.

The coordinates of a point in a cartesian plane is represented using its x and y coordinates. It is written as P(x,y), where x is the distance from the y-axis and y is the distance from x-axis. These two values are called the coordinates of a point. Let’s consider P and Q are two points on a cartesian plane with coordinates P(3, 4) and Q(-6, -2) respectively then, x1 = 3 and y1  = 4 and x2 = -6 and y2 = -2 are called coordinates of P and Q respective that can be represented graphically on a coordinate plane. Based on whether the value of x and y coordinates is positive or negative these points will locate in one of the following four coordinates. 
 

Four Quadrant of a Cartesian Plane

The relationship between the signs of the coordinates of a point and the quadrant of a point in which it lies in are as follows:

• First Quadrant(+ , +): If a point is in the 1st quadrant, then the point will be in the form (+, +), since the 1st quadrant is enclosed by the positive x - axis and the positive y - axis.

• Second Quadrant(− , +): If a point is in the 2nd quadrant, then the point will be in the form (–, +), since the 2nd quadrant is enclosed by the negative x - axis and the positive y - axis.

• Third Quadrant (− , −) : If a point is in the 3rd quadrant, then the point will be in the form (–, –), since the 3rd quadrant is enclosed by the negative x - axis and the negative y - axis.

• Fourth Quadrant (+ , −): If a point is in the 4th quadrant, then the point will be in the form (+, –), since the 4th quadrant is enclosed by the positive x - axis and the negative y - axis.

Keynotes: 

• Both the x and y axis do not belong to any quadrant.

• The coordinates of a points located on the x-axis are represented in general form as: (x, 0).

• The coordinates of a points located on the y-axis are represented in general form as: (0, y).

• The origin O(0, 0) where both the axes intersec each other belongs to no quadrant.
  
  

How to Plot Points on a Cartesian Plane

To plot any point on on cartesian plane like (1, −2) following two steps:

1. Move 1 units right along the x-axis, then 2 units down along the y-axis. 

2. The sign of each coordinate tells you the direction, and the number tells you the distance.
   
   

Solved Examples on Quadrant of a Cartesian Plane

Example 1: Plot the point A(3, 4) on the Cartesian plane.

Solution:

1. Start at the origin O(0, 0).
2. Move 3 units to the right along the x-axis (since x = 3 > 0).
3. From that position, move 4 units upward (since y = 4 > 0).
4. Mark the point and label it A(3, 4).

Answer: A(3, 4) lies in Quadrant I.

Example 2: A point M is located 5 units to the right of the y-axis and 3 units below the x-axis. Write its coordinates and quadrant.

Solution:

• 5 units to the right ⇒ x = 5 (positive)
• 3 units below ⇒ y = −3 (negative)

Answer: M = (5, −3), lying in Quadrant IV.

Example: Without plotting, determine the quadrant of each point:
(a) (−100, 200)
(b) (15, −15)
(c) (−3, −8)
(d) (0.5, 0.7)

Solution:

• (−100, 200): x < 0, y > 0 ⇒ Quadrant II
• (15, −15): x > 0, y < 0 ⇒ Quadrant IV
• (−3, −8): x < 0, y < 0 ⇒ Quadrant III
• (0.5, 0.7): x > 0, y > 0 ⇒ Quadrant I

Answer: Q-II, Q-IV, Q-III, Q-I respectively.