Understand the idea.
Two number lines meet
A coordinate grid combines two number lines. The horizontal axis is the -axis and the vertical axis is the -axis. They meet at the origin, , which is the reference for both directions.
An ordered pair gives horizontal position first and vertical position second. Positive is right and negative is left; positive is up and negative is down. Check the labelled scale on each axis.
Keep the order fixed
To locate , start at the origin, move three units left, then two units up. Read each sign with its own coordinate. The negative first coordinate does not make the second coordinate negative as well.
A zero coordinate means no movement in that direction. The point lies on the vertical axis, four units below the origin. Swapping the coordinates usually gives a different point because their roles are fixed.
See the method in action.
Worked example 1
Describe (−2,3) relative to the origin.
Worked solution
- 1
Read the horizontal coordinate first.
A negative horizontal coordinate means two units left of the origin.
- 2
Read the vertical coordinate second.
A positive vertical coordinate means three units up.
- 3
Combine the two directions.
The point is two units left and three units up from the origin.
2 units left and 3 units up.
Worked example 2
A point is 4 units right and 1 unit down. Write its coordinates.
Worked solution
- 1
Translate the horizontal direction.
Four units right gives a positive first coordinate.
- 2
Translate the vertical direction.
One unit down gives a negative second coordinate.
- 3
Write the ordered pair.
Coordinates are always written horizontal first, then vertical.
(4,−1).
Try it yourself.
Check your understanding
What does the minus sign mean in (5,−2)?
Show answer & reasoning
The point is 2 units below the horizontal axis.
The minus sign belongs to the second coordinate, so the point is two units below the horizontal axis. The first coordinate still places it five units right of the origin.
Keep practising
6 worksheet questions · 9 marks
Read the questions online
- Describe from the origin.1 mark
- Write coordinates for 2 left and 5 down.2 marks
- Which axis contains ?1 mark
- Is above or below the horizontal axis?2 marks
- Which is further left: or ?1 mark
- Leo writes 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 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.
. - Which axis contains ?1 mark
Its horizontal coordinate is zero.
The vertical -axis. - Is above or below the horizontal axis?2 marks
Its vertical coordinate is zero.
Neither; it is on the horizontal -axis. - Which is further left: or ?1 mark
Compare horizontal coordinates and .
. - Leo writes for 3 left and 2 up. Correct it.2 marks
Horizontal is and vertical is .
.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Positive/negative contexts; ordering; number lines; connection to coordinates.
Official curriculum source ↗