Coordinates, axes and a point's position
Read and plot ordered pairs, including negative coordinates and points on the axes.
Core and Extended.
Before you begin
- Locate positive and negative numbers on a number line.
- Read a labelled scale.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which number is two units to the left of zero?
What you will learn
- Interpret the horizontal and vertical coordinates in an ordered pair.
- Plot points in all four quadrants and on the axes.
- Use a grid's stated scale rather than counting squares as units.
Two number lines fix one position
The horizontal axis is the x-axis and the vertical axis is the y-axis. Their intersection is the origin, (0, 0). The ordered pair (x, y) gives horizontal position first and vertical position second. To plot (−3, 2), move three units left of the origin and then two units up. The order matters: (2, −3) is a different point.
Coordinates describe a location relative to the axes, rather than a journey you must literally draw. A point can be located by following either a horizontal or a vertical guide first, but its written pair is always x followed by y. Use a small cross or dot at the exact intersection and label it without covering nearby coordinates.
Signs and zeros tell you where to look
In the upper-right quadrant both coordinates are positive. Upper-left has negative x and positive y; lower-left has both negative; lower-right has positive x and negative y. For (4, 0), the vertical coordinate is zero, so the point lies on the x-axis. For (0, −5), the horizontal coordinate is zero, so it lies on the y-axis.
A point on an axis does not lie inside one of the four quadrants. Do not assign it a positive or negative sign merely because it is near a labelled region. A point's distance left or right is read from the origin, not from the edge of the page. A negative coordinate indicates direction, not a negative physical distance.
Read the scale before the position
If successive labelled x-values are 0, 2 and 4 with one square between them, one square represents two x-units. A point three squares to the right has x = 6. The y-axis may use a different scale, so check it separately. Counting three squares as three units would be wrong unless each square is labelled as one unit.
Coordinates can be fractional. Halfway between x = 1 and x = 2 means x = 1.5, even if no grid line is printed there. On a graph in context, the axes can represent quantities such as minutes and metres; state the units when interpreting a point. For ordinary Cartesian coordinates, write the ordered pair using parentheses and a comma.
Pause and explain
Where does (−4, 0) lie?
Worked example
A is 3 units left and 2 units above the origin. B lies on the y-axis 4 units below the origin. Write both coordinates.
Show the worked solution
- Left gives a negative horizontal coordinate: x_A = −3; above gives y_A = 2.
- On the y-axis means x_B = 0; below gives y_B = −4.
- Write horizontal position first in both pairs.
Answer A = (−3, 2), B = (0, −4)
From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Plot P = (−2, 3) and Q = (3, −2) on a grid. Describe their positions.
Give me a hint
Read x first, then y, and keep each sign.
Compare my reasoning
- P is two units left and three units up, in the upper-left quadrant.
- Q is three units right and two units down, in the lower-right quadrant.
- The swapped coordinates give different points; label both.
P: upper-left; Q: lower-right
Look for these in your work
- Used the coordinate order correctly.
- Placed the signs in the correct directions.
Write the coordinates of a point on the x-axis 5 units left of the origin and a point on the y-axis 2.5 units above it.
Give me a hint
One coordinate is zero on each axis.
Compare my reasoning
- The first point has x = −5 and y = 0.
- The second has x = 0 and y = 2.5.
- Write the pairs in the order (x, y).
(−5, 0) and (0, 2.5)
Look for these in your work
- Set the appropriate coordinate to zero.
- Retained the fractional vertical value.
A map grid uses 2 km per horizontal square and 0.5 km per vertical square. A shelter is 3 squares left and 4 squares up from the origin. Give its coordinates in kilometres.
Give me a hint
Multiply each square count by its own axis scale.
Compare my reasoning
- Horizontal position is −3 × 2 = −6 km.
- Vertical position is 4 × 0.5 = 2 km.
- The point is (−6, 2), with both coordinates measured in kilometres.
(−6, 2) km
Look for these in your work
- Applied each axis scale separately.
- Used signs for directions rather than negative distances.
Common mistakes
- Swapping x and y.
- Assuming each printed square represents one unit.
- Placing points with a zero coordinate inside a quadrant.
What can you explain now?
Which coordinate is zero for every point on the y-axis?
Compare with the explanation
The x-coordinate.
A point on the vertical axis has no horizontal displacement from the origin, so x = 0.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Tomorrow, plot three signed or fractional pairs on a blank grid and explain each direction. Include one point on an axis.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.
Original StudyForA teaching content · AI-assisted checks · Human teacher review pending.
Number contains 19 sequenced lessons; Algebra and graphs contains 21; Coordinate geometry contains 10 teaching lessons; Geometry contains 15. Coordinate geometry and Geometry each have a mixed checkpoint. Nine earlier overviews support selected topics across the syllabus. The other five syllabus areas, full cumulative assessment and human teacher review are not yet complete. Written lesson practice and paper constructions are self-checked, not automatically graded. The checkpoints sample skills and do not save an exam grade or certify mastery.
Check the official syllabus 2025–2027 Open related practice and resources