Learning Objectives
- read coordinates in the correct order;
- plot points in all four quadrants;
- identify points lying on an axis;
- check whether a plotted point is reasonable.
Introduction
This lesson develops Reading and Plotting Coordinates from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
🤔 Think About This...
Two students are asked to plot the point (3, 2).
The second student is correct because coordinates are always written in the order x, then y.
Plot the Coordinate
Click the grid where you think the requested point belongs.
How Do Coordinates Work?
| Point | x movement | y movement | Quadrant |
|---|---|---|---|
| A(4, 3) | 4 right | 3 up | I |
| B(−2, 5) | 2 left | 5 up | II |
| C(−3, −1) | 3 left | 1 down | III |
| D(5, −4) | 5 right | 4 down | IV |
Worked Example 1: Plotting a Point
Plot P(−3, 4).
Begin at the origin.
The x-coordinate is −3, so move 3 units left.
The y-coordinate is 4, so move 4 units up.
Mark and label the point P.
Points on the Axes
A point lies on the x-axis when its y-coordinate is zero. A point lies on the y-axis when its x-coordinate is zero.
⚠️ Common Mistake: Reversing Coordinates
✅ Quick Check
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Practice Questions
Foundation- Plot A(2, 4), B(−3, 1), C(−2, −4) and D(5, −1).
- State the quadrant containing each point.
- Write one point that lies on the x-axis.
- A point lies 4 units left and 6 units up from the origin. Write its coordinates.
- Point R is on the y-axis and 5 units below the origin. Write R.
- Plot four points that form a rectangle and write their coordinates.
✅ Check Your Work
Attempt the questions before opening the solutions.
Show answers and working
Foundation
- A(2,4) is in I; B(−3,1) is in II; C(−2,−4) is in III; D(5,−1) is in IV.
- I, II, III and IV respectively.
- Any point of the form (x,0), for example (4,0).
Developing
- (−4,6)
- R=(0,−5)
Challenge
- One possible answer is (1,1), (5,1), (5,4), (1,4).
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Coordinates are written (x, y).
- Move sideways first, then vertically.
- A zero y-coordinate places a point on the x-axis.
- A zero x-coordinate places a point on the y-axis.