Plot and read ordered pairs using the numbered axes
Read horizontal then vertical coordinates · Distinguish axes from quadrants · Use the numbered tick scale rather than just counting squares
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Signed numbers
- Horizontal and vertical directions
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Read horizontal then vertical coordinates
- Distinguish axes from quadrants
- Use the numbered tick scale rather than just counting squares
The order matters
A point (x,y) uses its horizontal coordinate first and its vertical coordinate second. From O, negative x moves left and positive y moves up. Plot (−3,2) by moving three units left then two up. Reversing the coordinates gives a different point.
In the four open quadrants the sign pairs are (+,+), (−,+), (−,−) and (+,−). A point with x=0 is on the y-axis, and one with y=0 is on the x-axis; axis points do not belong to an open quadrant.
Read the scale
Not every grid square represents one unit. In the Transfer diagram, x ticks increase by 2 and y ticks by 1. Two squares right and one down is (4,−1), not (2,−1). Read the numbered axes before interpreting a plotted point. Unequal axis scales are usable for position reading but should not be treated as equal physical distances.
Sources for this lesson
Pause and explain
Which axis contains a point whose x coordinate is zero?
Worked example
Read A in the first coordinate diagram.
Show the worked solution
- Its vertical projection reaches x=−3.
- Its horizontal projection reaches y=2; write x first.
Answer A(−3,2).
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →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.
Read A and B from the first diagram.
Give me a hint
Project to the numbered axes; read x first.
Compare my reasoning
- A is three left and two up.
- B is two right and one down.
A(−3,2); B(2,−1).
Look for these in your work
- Use the ordered-pair convention
- Read both signs
In the first diagram, C is at (0,3) and D at (−2,−2). State where each lies: an axis or an open quadrant.
Give me a hint
Check zero coordinates before quadrant signs.
Compare my reasoning
- C lies on the y-axis.
- D has two negative coordinates, so lies in the third quadrant.
C: y-axis; D: third quadrant.
Look for these in your work
- Handle axis points separately
- Use both signs
In the diagram below, a student counts two squares right and one down for E and writes (2,−1). Correct the coordinates using the numbered axes.
Give me a hint
One horizontal square is two x units.
Compare my reasoning
- Two horizontal squares give x=4.
- One downward square gives y=−1.
E(4,−1).
Look for these in your work
- Read each axis scale
- Do not infer units from square count alone
Common mistakes
- Keep the horizontal coordinate first.
- A point on an axis is not in an open quadrant.
What can you explain now?
Which axis contains a point whose x coordinate is zero?
Compare with the explanation
The y-axis.
Its horizontal displacement from the origin is zero, so it stays on the vertical axis.
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Make it stick
Which axis contains a point whose x coordinate is zero?
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.