year 8 maths

7A
The Cartesian plane
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7A The Cartesian plane
On a number plane, a pair of coordinates gives the exact position of a point. The number plane is also
called the Cartesian plane after its inventor, René Descartes, who lived in France in the 17th century.
The number plane extends both a horizontal axis (x) and vertical axis (y) to include negative numbers.
The point where these axes cross over is called the origin and it provides a reference point for all other
points on the plane.
Let’s start: Make the shape
In groups or as a class, see if you can remember how to plot points on a number plane. Then decide what
type of shape is formed by each set.
y
−4
−3 −2
4
3
2
1
−1
O
−1
−2
−3
−4
1 2 3 4
x
• A(0, 0), B(3, 1), C(0, 4)
• A(−2, 3), B(−2, −1), C(−1, −1), D(−1, 3)
• A(−3, −4), B(2, −4), C(0, −1), D(−1, −1)
Discuss the basic rules for plotting points on a number plane.
■ The Cartesian plane includes a vertical y -axis and a horizontal x -axis intersecting at right
angles. It is also called a number plane.
• There are four quadrants , labelled as shown.
■ A point on a number plane has coordinates (x, y) .
y
• The x -coordinate is listed first, followed by the
4
y -coordinate.
Quadrant 2 3 Quadrant 1
■ The point (0, 0) is called the origin .
2
1 (0, 0) Origin
horizontal vertical
■ (x, y) = units from , units from
( origin origin ) −4 −3 −2 −1
O
−1
1 2 3 4
−2
Quadrant 3 −3 Quadrant 4
−4
x
Key ideas
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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