Year 8 Interactive Maths - Second Edition

## The Cartesian Plane

The Cartesian plane consists of two directed lines that perpendicularly intersect their respective zero points.

The horizontal directed line is called the x-axis and the vertical directed line is called the y-axis.  The point of intersection of the x-axis and the y-axis is called the origin and is denoted by the letter O.

### The Coordinates

The position of any point on the Cartesian plane is described by using two numbers:  (x, y).  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.

For example, the ordered pair (5, 8) represents a point 5 units to the right of the origin in the direction of the x-axis and 8 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 5; and the y-coordinate of point P is 8.

###### Or simply, we can say that:

The coordinates of point P are (5, 8).

###### Note the following:
• For the point P(5, 8), the ordered pair is (5, 8).  So:
5 is the x-coordinate, and
8 is the y-coordinate.
• P(5, 8) means P is 5 units to the right of and 8 units above the origin.

#### Example 1

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

##### Solution:

A is 3 units to the right of and 2 units above the origin.  So, point A is (3, 2).
B
is 5 units to the right of and 5 units above the origin.  So, point B is (5, 5).
C
is 7 units to the right of and 8 units above the origin.  So, point C is (7, 8).
D
is 6 units to the left of and 4 units above the origin.  So, point D is (–6, 4).
E
is 3 units to the left of and 7 units above the origin.  So, point E is (–3, 7).
F
is 4 units to the left of and 6 units below the origin.  So, point F is (–4, –6).
G
is 8 units to the left of and 8 units below the origin.  So, point G is (–8, –8).
P
is 9 units to the right of and 9 units below the origin.  So, point P is (9, –9).
Q
is 6 units to the right of and 5 units below the origin.  So, point Q is (6, –5).