The idea, step by step
Two number lines meet
A coordinate grid has a horizontal x-axis and a vertical y-axis meeting at (0,0), the origin. The first coordinate describes horizontal position; the second describes vertical position.
Positive x is right and negative x is left. Positive y is up and negative y is down. Each coordinate is measured from its own zero line.
Keep the order fixed
To find (−3,2), go 3 units left, then 2 units up. The negative sign belongs only to the horizontal coordinate. Changing the coordinate order normally changes the position.
Points can lie on an axis. In (0,−4), the zero horizontal coordinate places the point on the vertical axis, four units below the origin. Full grid work follows in the Cartesian plane chapter.
A common trap
(−2,3) means 2 down and 3 right.
Instead: Read horizontal first: 2 left and 3 up.
See the thinking
Worked example 1
Describe (−2,3) relative to the origin.
- −2 is the horizontal coordinate, so move 2 left.
- 3 is the vertical coordinate, so move 3 up.
Worked example 2
A point is 4 units right and 1 unit down. Write its coordinates.
- Right gives x=4.
- Down gives y=−1.
Check your understanding
What does the minus sign mean in (5,−2)?
Show answer
The point is 2 units below the horizontal axis.
The second coordinate describes vertical position.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- Describe (3,−4) from the origin.1 mark
- Write coordinates for 2 left and 5 down.2 marks
- Which axis contains (0,6)?1 mark
- Is (−7,0) above or below the horizontal axis?2 marks
- Which is further left: (−4,1) or (−1,−3)?1 mark
- Leo writes (2,−3) for 3 left and 2 up. Correct it.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Describe (3,−4) from the origin.1 mark
Read horizontal, then vertical.
3 right and 4 down. - Write coordinates for 2 left and 5 down.2 marks
Both directions are negative.
(−2,−5). - Which axis contains (0,6)?1 mark
Its horizontal coordinate is zero.
The vertical y-axis. - Is (−7,0) above or below the horizontal axis?2 marks
Its vertical coordinate is zero.
Neither; it is on the horizontal x-axis. - Which is further left: (−4,1) or (−1,−3)?1 mark
Compare horizontal coordinates −4 and −1.
(−4,1). - Leo writes (2,−3) for 3 left and 2 up. Correct it.2 marks
Horizontal is −3 and vertical is +2.
(−3,2).
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Positive/negative contexts; ordering; number lines; connection to coordinates.
Official curriculum source ↗