Topics
3. Integers
topic badge
AustraliaNSW
Stage 3

3.05 Coordinate plane

Lesson
Practice
Lesson

Are you ready?

Let's remember how to read and plot positive coordinates in a coordinate plane.

Examples

Example 1

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.

So correct answer is B.

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

Coordinate plane

This video looks at all four quadrants of the coordinate plane.

Loading video...

Examples

Example 2

What are the coordinates of the point shown in the coordinate plane?

-5
-4
-3
-2
-1
1
2
3
4
5
x
-7
-6
-5
-4
-3
-2
-1
1
2
3
y
Worked Solution
Create a strategy

Count the number of horizontal and vertical units you need to move from the origin, and consider whether it is in the positive or negative direction.

Apply the idea

To get to this point from the origin, we need to move 3 units in the left (negative) direction, and 6 units down (negative direction).

The coordinates of the point are (-3,\,-6).

Example 3

Plot the point (-9,\,3) on the coordinate plane.

-9
-8
-7
-6
-5
-4
-3
-2
-1
1
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
Worked Solution
Create a strategy

The x-coordinate tells us how far left or right the point is from the origin. The y-coordinate tells us how far up or down the point is from the origin.

Apply the idea

Starting the origin (0,\,0), move 9 horizontal units in the left (negative) direction and then 3 vertical units in the upward (positive) direction.

-9
-8
-7
-6
-5
-4
-3
-2
-1
1
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
Idea summary

The coordinate plane has an x-axis which runs horizontally and a y-axis which runs vertically.

Each coordinate pair has an x-coordinate and a y-coordinate.

Outcomes

MA3-8NA

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

What is Mathspace

About Mathspace