The idea, step by step
Across, then up
An ordered pair such as (2, 4) gives two distances from the origin. The first number is x: move 2 units along the horizontal axis. The second number is y: move 4 units up.
Order matters. The points (2, 4) and (4, 2) usually occupy different places. Say “across first, then up” while you trace a path from the origin.
Points on an axis
A zero does not mean a point is missing. The point (0, 3) is on the y-axis because no horizontal movement is needed. The point (5, 0) is on the x-axis because no upward movement is needed.
To read a point, follow its vertical grid line down to x and its horizontal grid line across to y. Write the values in that order, with brackets and a comma.
A common trap
The numbers in (2, 5) can be swapped without changing the point.
Instead: The numbers have different roles: x measures across and y measures up.
See the thinking
Read a point
Read A on the supplied grid.
- Follow A down to x = 2.
- Follow A across to y = 4.
Plot an axis point
Where should (4, 0) be drawn?
- Move 4 units horizontally from the origin.
- The second value is zero, so do not move upwards.
Check your understanding
What does the zero in (0, 6) tell you?
Show answer
The point is on the y-axis.
Its horizontal distance from the origin is zero.
Your turn
6 questions · 7 marks · Work at your own pace.
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)
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Constructing grids; ordered coordinates; movement; translations/reflections/rotations; symmetry.
Official curriculum source ↗