# 3.04 Positive coordinates

Lesson

## Are you ready?

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.

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.

b

Plot 528 on the number line below.

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.

c

Plot 700 on the number line below.

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.

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.

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.

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.

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

### Outcomes

#### VCMMG230

Introduce the Cartesian coordinate system using all four quadrants