Ordered coordinates | Year 5

01 / LEARN

Understand the idea.

Across, then up

An ordered pair records a point as $(x, y)$ . On these positive grids, the first coordinate tells how far across to go from the origin, and the second tells how far up.

Read the axis labels rather than assuming one square is one unit. To read a point, trace vertically to the horizontal axis for $x$ , then horizontally to the vertical axis for $y$ . Write across first.

An equal-unit coordinate grid labelled from zero to six on both axes, with A at (2, 4), B at (5, 1) and C at (0, 3).

Points on an axis

A zero coordinate still gives useful information. At $(0, 3)$ there is no horizontal movement, so the point stays on the $y$ -axis. At $(5, 0)$ there is no upward movement, so it lies on the $x$ -axis.

The order fixes the roles of the numbers. Swapping $(2, 4)$ to $(4, 2)$ usually changes the location, because the horizontal and vertical distances are exchanged. Keep the brackets and comma to show one ordered pair.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Read a point

Read A on the supplied grid.

Worked solution

1
Read the horizontal position of A.
$x = 2$
Following its vertical grid line to the x-axis gives the across coordinate.
2
Read its vertical position.
$y = 4$
Following its horizontal grid line to the y-axis gives the height coordinate.
3
Write the ordered pair.
$A = (2, 4)$
The horizontal value is written first and the vertical value second.

Answer

A is (2, 4).

EXAMPLE 02

Plot an axis point

Where should (4, 0) be drawn?

Worked solution

1
Follow the first coordinate.
$x = 4$
Move four units across from the origin along the horizontal axis.
2
Follow the second coordinate.
$y = 0$
Zero height means there is no upward movement from the axis.
3
Mark the resulting point.
$(4, 0)$
The point lies at 4 on the x-axis, not four units up the y-axis.

Answer

On the x-axis at 4.

03 / YOUR TURN

Try it yourself.

Check your understanding

What does the zero in (0, 6) tell you?

Show answer & reasoning

The point is on the y-axis.

In $(0, 6)$ , $x = 0$ means there is no horizontal displacement from the origin. The height is 6, so the point lies on the y-axis.

Keep practising

6 worksheet questions · 7 marks

Open worksheet Worked solutions

Read the questions online

Read B on the grid.
1 mark
Read C on the grid.
1 mark
Plot and label $P (3, 5)$ on the supplied grid.
1 mark
Which point lies on the x-axis: $(0, 4)$ , $(4, 0)$ or $(4, 4)$ ?
1 mark
Are $(1, 6)$ and $(6, 1)$ the same point? Explain.
2 marks
A point is 2 units above the origin and has x-coordinate 5. Write its coordinates.
1 mark

Read the worked solutions

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

Read B on the grid.
1 mark
B is 5 across and 1 up.
$(5, 1)$
Read C on the grid.
1 mark
C is on the y-axis at height 3.
$(0, 3)$
Plot and label $P (3, 5)$ on the supplied grid.
1 mark
Use $x = 3$ first and $y = 5$ second.
P at the intersection 3 across and 5 up.
Which point lies on the x-axis: $(0, 4)$ , $(4, 0)$ or $(4, 4)$ ?
1 mark
A point on the x-axis has $y = 0$ .
$(4, 0)$
Are $(1, 6)$ and $(6, 1)$ the same point? Explain.
2 marks
Swapping coordinate roles changes the location.
No. One is 1 across and 6 up; the other is 6 across and 1 up.
A point is 2 units above the origin and has x-coordinate 5. Write its coordinates.
1 mark
Put the horizontal coordinate first.
$(5, 2)$

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics 2026

Constructing grids; ordered coordinates; movement; translations/reflections/rotations; symmetry.

Official curriculum source ↗

In this lesson

Understand the idea.

Across, then up

Points on an axis

See the method in action.

Read a point

Read the horizontal position of A.

Read its vertical position.

Write the ordered pair.

Plot an axis point

Follow the first coordinate.

Follow the second coordinate.

Mark the resulting point.

Try it yourself.

Check your understanding

Keep practising