YEAR 7 · COORDINATES, PATTERNS AND GRAPHS · 15 MIN

Four-quadrant coordinates

Use ordered pairs and signs to locate points in all four quadrants.

In this lesson

Read the horizontal coordinate first
Identify quadrants and points on axes

Before you start

Positive and negative numbers
Number lines

01 / LEARN

Understand the idea.

Two numbers identify one point

An ordered pair $(x, y)$ locates a point from the origin $(0, 0)$ . Read the horizontal coordinate first: positive means right and negative means left. Then use the vertical coordinate: positive means up and negative means down.

Coordinates describe position, not an addition of the two numbers. Swapping them usually changes the location: $(2, 4)$ is $2$ units right and $4$ up, while $(4, 2)$ is $4$ right and $2$ up.

Square coordinate grid from minus five to five on both axes. A is three-two, B is minus three-two, C is minus three-minus two and D is three-minus two.

Quadrants and boundaries

The axes divide the plane into four quadrants. Starting in the top-right and moving anticlockwise, their sign pairs are I $(+, +)$ , II $(-, +)$ , III $(-, -)$ and IV $(+, -)$ . Use both signs to identify the region.

A zero coordinate places the point on a boundary: $x = 0$ means the $y$ -axis, and $y = 0$ means the $x$ -axis. Axis points belong to no quadrant. The origin is the point where both coordinates are zero.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Left, then up

Which quadrant contains $(- 3, 2)$ ?

Worked solution

1
Read the horizontal coordinate.
$x = - 3$
A negative horizontal coordinate places the point 3 units left of the origin.
2
Read the vertical coordinate.
$y = 2$
A positive vertical coordinate places the point 2 units above the origin.
3
Identify the sign pair.
$(-, +)$
Left and above is quadrant II.

Answer

Quadrant II.

EXAMPLE 02

A point on a boundary

Describe the position of $(0, - 4)$ .

Worked solution

1
Check the horizontal coordinate.
$x = 0$
With no left or right displacement, the point is on the y-axis.
2
Use the vertical coordinate.
$y = - 4$
The point is 4 units below the origin on the negative part of that axis.
3
Classify the position.
The axes are quadrant boundaries, so this point is not inside any quadrant.

Answer

On the y-axis, not inside a quadrant.

03 / YOUR TURN

Try it yourself.

Check your understanding

Which quadrant contains $(5, - 1)$ ?

Show answer & reasoning

Quadrant IV.

The signs of $(5, - 1)$ are $(+, -)$ . The point is right of the origin and below it, which places it in quadrant IV.

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

Describe the moves from the origin to $(4, 1)$ .
2 marks
Name the quadrant containing $(- 2, - 5)$ .
2 marks
A point is 3 left and 4 up from the origin. Write its coordinates.
2 marks
Which axis contains $(6, 0)$ ?
2 marks
Is the origin in quadrant I? Explain.
2 marks
Can a point with positive $x$ and negative $y$ lie in quadrant II? Explain.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Describe the moves from the origin to $(4, 1)$ .
2 marks
Read $x = 4$ before $y = 1$ .
4 right, then 1 up.
Name the quadrant containing $(- 2, - 5)$ .
2 marks
Both coordinates are negative: left and down.
Quadrant III.
A point is 3 left and 4 up from the origin. Write its coordinates.
2 marks
Left gives $x = - 3$ ; up gives $y = 4$ .
$(- 3, 4)$
Which axis contains $(6, 0)$ ?
2 marks
Its y-coordinate is zero.
The x-axis.
Is the origin in quadrant I? Explain.
2 marks
At $(0, 0)$ , neither coordinate is positive or negative.
No. It lies on both axes.
Can a point with positive $x$ and negative $y$ lie in quadrant II? Explain.
2 marks
Quadrant II needs negative $x$ and positive $y$ .
No. Those signs place it in quadrant IV.

Checking saved progress…

Curriculum reference & lesson scope

Australian Curriculum v9.0 / South Australian Curriculum

Year 7 coordinate, pattern and authentic-graph interpretation scope. Includes prerequisite four-quadrant plotting; formal gradient/intercept techniques are not required here.

Official curriculum source ↗

In this lesson

Understand the idea.

Two numbers identify one point

Quadrants and boundaries

See the method in action.

Left, then up

Read the horizontal coordinate.

Read the vertical coordinate.

Identify the sign pair.

A point on a boundary

Check the horizontal coordinate.

Use the vertical coordinate.

Classify the position.

Try it yourself.

Check your understanding

Keep practising