The right-bottom side region in the two dimensional space is called the fourth quadrant.

## Introduction

Two number lines get bisected perpendicularly at their middle point in two-dimensional Cartesian coordinate system to split the coordinate plane into four equal regions.

The right-bottom side region is called the fourth quadrant. In this case, the region in the angle $XOY’$ is the fourth quadrant and represented by a Roman numeral $IV$.

In $\angle XOY’$, the $x$-axis represents positive values and $y$-axis represents negative values. The signs of both abscissa and ordinate of each point in this region should be positive and negative respectively.

If $x$-coordinate and $y$-coordinate of every point are denoted by $x$ and $y$ respectively, then the values of them are written mathematically as $x > 0$ and $y < 0$.

### Usage

In two dimensional space, the fourth quadrant is used to identity the location of a point whose abscissa is positive and ordinate is negative. Let’s begin it to learn how to use the fourth quadrant in the coordinate geometry.

#### Example

Identify the location of the point $D(5, -3)$.

The $x$ coordinate (or abscissa) is $5$ and $y$ coordinate (or ordinate) is $-3$ in this example.

1. Identity $5$ on positive $x$-axis. Draw a line from $5$ but it should be parallel to negative $y$ axis and perpendicular to positive $x$ axis.
2. Identify $-3$ on negative $y$ axis. Draw a line from $-3$ but it should be perpendicular to negative $y$ axis and parallel to positive $x$ axis.
3. The two lines get intersected perpendicularly at a point in the plane and it is the point $D(5, -3)$.

In this way, the fourth quadrant of bi dimensional Cartesian coordinate system is used for identifying the location of any point whose abscissa is positive and ordinate is negative.

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Jun 26, 2023

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