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Mathematics
The Cartesian Plane | Elementary

The Cartesian Plane - Cycle 2

| Mathematics
1-2
3-4
5-6
Table of contents

What is a Cartesian Plane?

Definition

The Cartesian plane is a reference system.

Example:

Exemple de plan cartésien

The Cartesian plane is made up of a horizontal and a vertical axis.

Each axis is graduated using numbers. The horizontal axis is read from 0 towards the right, and the vertical axis is read from 0 upwards.

Example
The horizontal axis and the vertical axis of the Cartesian plane
Find out more!

The horizontal axis is also called the x-axis, and the vertical axis, the y-axis.

What are Coordinates?

Definition

Coordinates are numbers that specify the horizontal or vertical position of a point on the Cartesian plane.

A horizontal coordinate represents the position of a point on the horizontal axis.

A vertical coordinate represents its position on the vertical axis.

Example

Example of a point on the Cartesian plane.

The horizontal coordinate of the point is 3.
The vertical coordinate of the point is 5.

What is an Ordered Pair?

An ordered pair is used to find the exact position of a point on a Cartesian plane. Write the horizontal coordinate followed by the vertical coordinate between brackets. Separate the two coordinates by a comma.

Example
Example of an ordered pair

What is the Origin?

Definition

The origin is the point where the horizontal and vertical axes meet. It is represented by the coordinates (0, 0).

Example:

The origin on a Cartesian plane.

How Do You Place a Point on the Cartesian Plane From its Coordinates?

Rule

To place a point on the Cartesian plane using its coordinates, follow these steps:

  1. Look at the first coordinate in the ordered pair and find the line corresponding to this number on the horizontal axis.
  2. Look at the second coordinate in the ordered pair and find the line corresponding to this number on the vertical axis.
  3. Place the point where the two lines meet.
Example

Place the point with coordinates (4, 2) on the Cartesian plane.

  1. Look at the first coordinate in the ordered pair and find the line corresponding to this number on the horizontal axis.

    In the ordered pair (4, 2), the first coordinate is 4.

Example of a Cartesian plane.

  1. Look at the second coordinate in the ordered pair and find the line corresponding to this number on the vertical axis.

    In the ordered pair (4, 2), the second coordinate is 2.

Example of a Cartesian plane.
  1. Place the point where the two lines meet.
Example of a Cartesian plane.
Example

Place the point with coordinates (0, 5) on the Cartesian plane.

  1. Look at the first coordinate in the ordered pair and find the line corresponding to this number on the horizontal axis.

    In the ordered pair (0, 5), the first coordinate is 0.

Example of a Cartesian plane.

  1. Look at the second coordinate in the ordered pair and find the line corresponding to this number on the vertical axis.

    In the ordered pair (0, 5), the second coordinate is 5.

Example of a Cartesian plane.
  1. Place the point where the two lines meet.
Example of a Cartesian plane.

How Do You Find the Position of a Point on a Cartesian Plane?

Rule

To find the position of a point on the Cartesian plane, follow these steps:

  1. Find the horizontal coordinate of the point.
  2. Find the vertical coordinate of the point.
  3. Write the ordered pair with the horizontal coordinate followed by the vertical coordinate in brackets, and separate them by a comma.
Example

Find the position of the point on the following Cartesian plane.

Example of a point on a Cartesian plane.

  1. Find the horizontal coordinate of the point.

    The point is on the line corresponding with the number 2 on the horizontal axis.

Example of a Cartesian plane.

  1. Find the vertical coordinate of the point.

    The point is on the line corresponding with the number 3 on the vertical axis.

Example of a Cartesian plane.
  1. Write the ordered pair with the horizontal coordinate followed by the vertical coordinate in brackets, and separate them by a comma.
(2, 3)
Example

Find the position of the point on the following Cartesian plane.

Example of a point on a Cartesian plane.

  1. Find the horizontal coordinate of the point.

    The point is on the line corresponding with the number 5 on the horizontal axis.

Example of a Cartesian plane.

  1. Find the vertical coordinate of the point.

    The point is on the line corresponding with the number 0 on the vertical axis.

Example of a Cartesian plane.
  1. Write the ordered pair by placing the horizontal and vertical coordinates in brackets, and separate them by a comma.
(5, 0)

See Also