Math Doubts

y-axis of two dimensional Cartesian coordinate system

A number line that displayed in vertical position in a two-dimensional Cartesian coordinate system is called the $y$-axis of two dimensional space.

Introduction

In Bi-dimensional Cartesian coordinate system, there are two number-lines, which are bisected at their middle point but one of them is drawn vertically for measuring the distance of a point from origin in vertical direction. Therefore, the number-line is called the $y$-axis of the two dimensional Cartesian coordinate system.

Example

The $y$-axis is represented by a number-line $YOY’$ in this example. The arrows above and below in number-line $\overleftrightarrow{YY’}$ represents that the straight line can be extended infinitely in both directions.

y axis of two dimensional space

Parts

In two-dimensional space, the horizontal number-line divides the $y$-axis as two parts at origin $(O)$.

Positive y-axis

The part of the $y$-axis that appears above the origin is called the positive $y$-axis. In this case, the ray $\overrightarrow{OY}$ represents the positive $y$-axis. Every division in the positive $y$-axis is denoted by the positive integers.

Negative y-axis

The part of the $y$-axis that appears below the origin is called the negative $y$-axis. In this case, the ray $\overrightarrow{OY’}$ denotes the negative $y$-axis. Each division in the negative $y$-axis is represented by the negative integers.

Usage

In two-dimensional space, the $y$-axis is used to know the distance of any point from the origin by comparing the vertical distance of the point with the number line on the $y$-axis. For example, $E$, $F$, $G$ and $H$ are four points in a two-dimensional Cartesian coordinate system.

points y axis of two dimensional space
  1. The point $E$ is a right side point to the positive $y$-axis and it is $1$ units away from the origin.
  2. The point $F$ is a right side point to the negative $y$-axis and it is $3$ units away from the origin.
  3. The point $G$ is a left side point to the positive $y$-axis and it is $2$ units away from the origin.
  4. The point $H$ is a left side point to the negative $y$-axis and it is $2$ units away from the origin.

In this way, the $y$-axis is used to measure the distance of any point from the origin in vertical direction by the comparison.

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