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■ In mathematics, a number plane is generally referred to as a Cartesian plane, named after the famous French mathematician, René Descartes (1596–1650).

■ A number plane consists of two straight perpendicular number lines, called axes.

• The horizontal number line is known as the x-axis.

• The vertical number line is known as the y-axis.

■ The point at which the two axes intersect is called the origin, and is often labelled O.

■ The position of a point on a number plane is given as a pair of numbers, known as the coordinates of the point. Coordinates are always written in brackets and the numbers are separated by a comma.

For example: (2, 4)

• The x-coordinate (input) is always written first. The x-coordinate indicates how far to go from the origin in the horizontal direction.

• The y-coordinate (output) is always written second. The y-coordinate indicates how far to go from the origin in the vertical direction.

Building Understanding

1 Which of the following is the correct way to describe point A?

D (x2, y1) E (1, 2) a The horizontal axis is known as the __________. b The _____________ is the vertical axis. c The point at which the axes intersect is called the ____________. d The x-coordinate is always written __________. e The second coordinate is always the ___________. f ________ comes before ________ in the dictionary, and the ________ coordinate comes before the ________ coordinate on the Cartesian plane.

2 Copy and complete the following sentences.

Example 23 Plotting points on a number plane

Draw a Cartesian plane, with both axes labelled from 0 to 5