The idea, step by step
Two directions from the origin
The Cartesian plane has a horizontal x-axis and a vertical y-axis. They meet at the origin, (0,0). An ordered pair (x,y) tells you to move horizontally first, then vertically. Positive x is right; negative x is left. Positive y is up; negative y is down.
The axes divide the plane into four regions called quadrants. Quadrant I is top right, II top left, III bottom left and IV bottom right. Their coordinate signs are (+,+), (−,+), (−,−) and (+,−).
Points on an axis
A point on the x-axis has y = 0. A point on the y-axis has x = 0. These points are on the boundaries and are not inside a quadrant. The origin belongs to both axes.
Always inspect the coordinate values rather than only the point’s label. For example, (0,−3) is on the y-axis below the origin; it is not in Quadrant III or IV.
A common trap
Putting a point into a quadrant whenever one coordinate is positive or negative, even if the other is zero.
Instead: Check for zero first. Points on an axis do not lie inside a quadrant.
See the thinking
Read the signs
Which quadrant contains (−3,2)?
- The x-coordinate is negative, so move left.
- The y-coordinate is positive, so move up.
- Left and up is the top-left region.
A point on a boundary
Locate (4,0). Is it in Quadrant I or IV?
- Move 4 units right from the origin.
- The vertical coordinate is 0, so stay on the horizontal axis.
Check your understanding
Which quadrant contains (2,−5)?
Show answer
Quadrant IV
Positive x moves right and negative y moves down.
Your turn
6 questions · 8 marks · Work at your own pace.
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.
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 ↗