Topics
13. Location and transformation
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AustraliaNSW
Stage 3

13.02 Number plane

Lesson
Practice
Lesson

Are you ready?

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Number lines help us work out distance and direction, and can be horizontal or vertical (think of a thermometer). Remembering how to plot points on a number line, will help us in this lesson.

Examples

Example 1

Plot the following numbers on the number lines:

a

Plot 3 on the number line below.

012345678910
Worked Solution
Create a strategy

Plot the point on the matching number.

Apply the idea

To plot 3, we can start at zero and jump right 3 spaces.

012345678910
b

Plot 528 on the number line below.

520525530
Worked Solution
Create a strategy

There are 5 spaces between 520 and 525, so each space represents in increase of 1 unit.

Apply the idea

538 is 3 more than 525.

To plot 528 we can start at 525 and jump right 3 spaces.

520525530
c

Plot 700 on the number line below.

05001000
Worked Solution
Create a strategy

There are 5 spaces between 0 and 500, so each space represents in increase of 100 units.

Apply the idea

700 is 200 more than 500.

To plot 700 we can start at 500 and jump right 2 spaces.

05001000
Idea summary

Number lines help us work out distance and direction, and can be horizontal or vertical.

Positive coordinates on a number plane

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Examples

Example 2

Plot the point (0, 0) onto the coordinate plane.

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x
1
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9
y
Worked Solution
Create a strategy

The first number in a pair of coordinates tells us how many spaces to move across from the origin. The second number tells us how many spaces to move up or down from the origin.

Apply the idea

The point on the plane described by (0,\,0) is the origin.

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x
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y
Idea summary

The first number in a pair of coordinates tells us how many spaces to move across from the origin. The second number tells us how many spaces to move up or down from the origin.

Read and plot points with positive coordinates

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Examples

Example 3

Here is a number plane.

An image showing a coordinate plane with different objects plotted on it. Ask your teacher for more information.
a

What object has coordinates (6,\,2)?

A
Star
B
Bike
C
Dog
D
Apple
Worked Solution
Create a strategy

From the origin, move right the number of spaces as the first number, and move up the number of spaces as the second number.

Apply the idea

Starting from (0, 0), if we move 6 spaces to the right, then 2 spaces up, we will land on the bike.

The correct option is B: Bike.

b

What are the coordinates of the rabbit?

Worked Solution
Create a strategy

The number below the rabbit will be the first number in the coordinates. The number to the left of the rabbit will be the second number.

Apply the idea

The number below the rabbit is 9, and the number to the left of the rabbit is 8.

So the coordinates of the rabbit is (9,\,8).

Idea summary

Important terms to remember for a coordinate plane:

  • axes - the horizontal and vertical lines, the x-axis and y-axis

  • quadrants - the four different sections our axes create

  • coordinates - these tell us where points are located, with an x-value and a y-value

  • origin - where both x and y are equal to 0 and it's where both axes meet

Outcomes

MA3-8NA

analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane

MA3-17MG

locates and describes position on maps using a grid-reference system

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