Math Doubts

Third Quadrant

The left-bottom side region in the two dimensional space is called the third quadrant.

Introduction

third quadrant

Two number lines are perpendicularly bisected at their middle point in bi-dimensional Cartesian coordinate system for splitting the coordinate plane into four equal regions.

The left-bottom side region is called the third quadrant. In this case, the region in the angle $X’OY’$ is the third quadrant and represented by a Roman numeral $III$.

In $\angle X’OY’$, the $x$-axis and $y$-axis both represent negative values. Therefore, the abscissa and ordinate of every point in this region should be negative.

If $x$-coordinate and $y$-coordinate of each point are denoted by $x$ and $y$ respectively, then the values of both coordinates are written in mathematical form as $x < 0$ and $y < 0$.

Usage

The third quadrant is used in the bi dimensional space to identity the location of a point whose abscissa and ordinate are negative. So, let’s study how to use the third quadrant in coordinate geometry.

Example

Identify the location of the point $C(-6, -4)$.

third quadrant

Here, the $x$ coordinate (or abscissa) is $-6$ and $y$ coordinate (or ordinate) is $-4$.

  1. Identity $-6$ on negative $x$-axis. Draw a line from $-6$ but it should be parallel to negative $y$ axis and perpendicular to negative $x$ axis.
  2. Identify $-4$ on negative $y$ axis. Draw a line from $-4$ but it should be perpendicular to negative $y$ axis and parallel to negative $x$ axis.
  3. The two straight lines are perpendicularly intersected at a point in the plane and it is the point $C(-6, -4)$.

In this way, the third quadrant of two dimensional Cartesian coordinate system is used for identifying the location of any point whose both abscissa and ordinate are negative.

Math Doubts
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more