The four coordinate quadrants | Year 6

01 / LEARN

Understand the idea.

Two directions from the origin

The horizontal $x$ -axis and vertical $y$ -axis meet at the origin, $(0, 0)$ . An ordered pair $(x, y)$ gives horizontal position first and vertical position second. Positive values mean right or up; negative values mean left or down.

The axes divide the plane into four quadrants. Start with Quadrant I in the top right and count anticlockwise. The sign pairs are I: $(+, +)$ , II: $(-, +)$ , III: $(-, -)$ and IV: $(+, -)$ .

Equal-unit Cartesian grid from negative five to five on both axes. A is at (3,3), B at (-3,3), C at (-3,-3) and D at (3,-3).

Points on an axis

Check for a zero coordinate before choosing a quadrant. If $y = 0$ , the point lies on the $x$ -axis. If $x = 0$ , it lies on the $y$ -axis. Points on an axis are boundaries between quadrants, rather than inside one.

The origin lies on both axes. A point such as $(0, - 3)$ is below the origin on the $y$ -axis: the zero horizontal coordinate keeps it on that axis, even though its vertical coordinate is negative.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Read the signs

Which quadrant contains (−3,2)?

Equal-unit Cartesian grid from minus five to five on both axes, with P at minus three, two. Only the point label is drawn; quadrant names are not supplied.

Worked solution

1
Read the horizontal coordinate.
$x = - 3 < 0$
A negative horizontal coordinate places the point left of the vertical axis.
2
Read the vertical coordinate.
$y = 2 > 0$
A positive vertical coordinate places the point above the horizontal axis.
3
Name the region.
$(-, +) Quadrant II$
Left and above is the top-left quadrant, numbered II.

Answer

Quadrant II.

EXAMPLE 02

A point on a boundary

Locate (4,0). Is it in Quadrant I or IV?

Equal-unit Cartesian grid from minus five to five on both axes, with Q at four, zero on the horizontal axis.

Worked solution

1
Move to the horizontal position.
$x = 4$
The point is four units right of the origin.
2
Inspect the vertical coordinate.
$y = 0$
There is no movement above or below the horizontal axis.
3
Classify the location.
$(4, 0) lies on the x -axis$
An axis is a boundary, so this point belongs to neither Quadrant I nor Quadrant IV.

Answer

It is on the x-axis, in neither quadrant.

03 / YOUR TURN

Try it yourself.

Check your understanding

Which quadrant contains (2,−5)?

Show answer & reasoning

Quadrant IV

For $(2, - 5)$ , positive $x$ means right and negative $y$ means down. That is the bottom-right region, Quadrant IV.

Keep practising

6 worksheet questions · 8 marks

Open worksheet Worked solutions

Read the questions online

Name the quadrant containing $(2, 3)$ .
1 mark
Name the quadrant containing $(- 4, 1)$ .
1 mark
Name the quadrant containing $(- 2, - 3)$ .
1 mark
Name the quadrant containing $(3, - 4)$ .
1 mark
Describe the location of $(0, - 2)$ . State whether it lies in a quadrant.
2 marks
Leo says $(- 5, 0)$ is in Quadrant III because it is to the left. Explain the error.
2 marks

Read the worked solutions

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

Name the quadrant containing $(2, 3)$ .
1 mark
Both coordinates are positive: right and up.
Quadrant I
Name the quadrant containing $(- 4, 1)$ .
1 mark
Negative $x$ and positive $y$ mean left and up.
Quadrant II
Name the quadrant containing $(- 2, - 3)$ .
1 mark
Both coordinates are negative: left and down.
Quadrant III
Name the quadrant containing $(3, - 4)$ .
1 mark
Positive $x$ and negative $y$ mean right and down.
Quadrant IV
Describe the location of $(0, - 2)$ . State whether it lies in a quadrant.
2 marks
$x = 0$ places the point on the $y$ -axis.
On the $y$ -axis, 2 units below the origin; no quadrant.
Leo says $(- 5, 0)$ is in Quadrant III because it is to the left. Explain the error.
2 marks
The $y$ -coordinate is zero, so the point is on a boundary.
Quadrant III requires both $x$ and $y$ to be negative.
It is on the $x$ -axis, not in Quadrant III.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Year 6 four-quadrant Cartesian coordinates, plotting and reading points, and coordinate changes.

Official curriculum source ↗

In this lesson

Understand the idea.

Two directions from the origin

Points on an axis

See the method in action.

Read the signs

Read the horizontal coordinate.

Read the vertical coordinate.

Name the region.

A point on a boundary

Move to the horizontal position.

Inspect the vertical coordinate.

Classify the location.

Try it yourself.

Check your understanding

Keep practising