G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

Order a 12-month Year 7 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 8 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 9 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 10 Interactive Maths software Homework Licence for only $19.95.

Year 7 Interactive Maths - Second Edition


The Cartesian Plane

The position of a point on a Cartesian plane is represented by referring to it in terms of a horizontal line and a vertical line, which are called the x-axis and y-axis respectively.  The point of intersection of the x-axis and the y-axis is called the origin.

Cartesian plane with the x-axis, y-axis and origin marked

Often, we draw a set of axes on graph paper as shown below.

Cartesian plane on graph paper

The position of any point on the Cartesian plane is described by using two numbers, (x, y), that are called coordinates.  The first number, x, is the horizontal position of the point from the origin.  It is called the x-coordinate. The second number, y, is the vertical position of the point from the origin.  It is called the y-coordinate.  Since a specific order is used to represent the coordinates, they are called ordered pairs.

Cartesian plane with the point P(x, y) marked

For example, an ordered pair (4, 5) represents a point 4 units to the right of the origin in the direction of the x-axis, and 5 units above the origin in the direction of the y-axis as shown in the diagram below.

We say that:

The x-coordinate of point P is 4; and the y-coordinate of point P is 5.

Or simply, we can say that:

The coordinates of point P are (4, 5).

Cartesian plane with the point P(4, 5) marked


Note the following:
  • For the point P(4, 5), the ordered pair is (4, 5).  So:
    4 is the x-coordinate, and
    5 is the y-coordinate.
  • P(4, 5) means P is 4 units to the right of and 5 units above the origin.


Example 3

State the coordinates of each of the points shown on the Cartesian plane:

Cartesian plane

Solution:

A is 1 unit to the right of and 2 units above the origin.  So, point A is (1, 2).
B
is 2 units to the right of and 3 units above the origin.  So, point B is (2, 3).
C
is 2 units to the right of and 4 units above the origin.  So, point C is (2, 4).
D
is 3 units to the right of and 4 units above the origin.  So, point D is (3, 4).
E
is 5 units to the right of and 2 units above the origin.  So, point E is (5, 2).
F
is 7 units to the right of and 3 units above the origin.  So, point F is (7, 3).
G
is 4 units to the right of and 5 units above the origin.  So, point G is (4, 5).
H
is 5 units to the right of and 6 units above the origin.  So, point H is (5, 6).
I
is 1 unit to the right of and 7 units above the origin.  So, point I is (1, 7).
J
is 7 units to the right of and 7 units above the origin.  So, point J is (7, 7).


Key Terms

point, Cartesian plane, horizontal line, x-axis, vertical line, y-axis, origin, axes, x-coordinate, y-coordinate, coordinates, ordered pairs, vertical position, horizontal position


| Home Page | Order Maths Software | About the Series | Maths Software Tutorials |
| Year 7 Maths Software | Year 8 Maths Software | Year 9 Maths Software | Year 10 Maths Software |
| Homework Software | Tutor Software | Maths Software Platform | Trial Maths Software |
| Feedback | About mathsteacher.com.au | Terms and Conditions | Our Policies | Links | Contact |

Copyright 2000-2019 mathsteacher.com Pty Ltd.  All rights reserved.
Australian Business Number 53 056 217 611

Copyright instructions for educational institutions

Please read the Terms and Conditions of Use of this Website and our Privacy and Other Policies.
If you experience difficulties when using this Website, tell us through the feedback form or by phoning the contact telephone number.