Write the coordinates of point A.
Count across (x) then up (y).
The point is 2 right and 2 up → (2, 2).
Coordinates
Coordinates describe positions on a grid using ordered pairs. This topic links geometry and algebra, and is essential for linear graphs and distance calculations.
Overview
Coordinates tell you the exact position of a point on a grid.
A coordinate is written as two numbers inside brackets.
\( (x, y) \)
The first number tells you how far to move along the horizontal axis. The second number tells you how far to move up or down the vertical axis.
What you should understand after this topic
- Read coordinates correctly
- Plot points on a grid
- Understand the x-axis and y-axis
- Understand how the four quadrants work
- Describe simple movements between points
Key Definitions
Coordinate
A pair of numbers that gives the position of a point.
x-coordinate
The first number. It shows horizontal position.
y-coordinate
The second number. It shows vertical position.
x-axis
The horizontal axis.
y-axis
The vertical axis.
Origin
The point where the axes cross: \( (0,0) \).
Key Rules
x first, y second
Always read coordinates as \( (x, y) \), never the other way round.
Start from the origin
Plot coordinates by moving from \( (0,0) \).
Horizontal before vertical
Move along the x-axis first, then up or down for the y-value.
Negative values matter
Negative x means left, negative y means down.
How to Solve
Step 1: Understand the axes
The coordinate plane is made of two perpendicular axes. The x-axis runs horizontally and the y-axis runs vertically. They meet at the origin.
Origin = \( (0,0) \)
Exam tip: Always check which axis is which before reading coordinates.
Step 2: Read coordinates in the correct order
Coordinates are always written as \( (x, y) \).
Move along the x-axis first (left or right).
Then move along the y-axis (up or down).
Exam tip: Across first, then up.
Step 3: Plotting a point
To plot \( (-3,5) \):
Move 3 left (negative x-value).
Move 5 up (positive y-value).
Mark the point clearly.
Step 4: Quadrants
The grid is divided into four quadrants.
Exam tip: Learn the sign pattern — this is frequently tested.
Quadrant 1
\( (+,+) \)
Quadrant 2
\( (-,+) \)
Quadrant 3
\( (-,-) \)
Quadrant 4
\( (+,-) \)
Step 5: Reading a point from a graph
Start at the point and read across first, then up or down.
Across gives the x-coordinate.
Up or down gives the y-coordinate.
Step 6: Distance on a grid
You can measure horizontal and vertical distances using coordinates.
Horizontal distance = difference in x-values.
Vertical distance = difference in y-values.
For diagonal distance, use Pythagoras’ theorem.
Step 7: Midpoint of a line
The midpoint is the point exactly halfway between two coordinates.
\( \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \)
Exam tip: Average x-values and y-values separately.
Example Questions
Edexcel
Exam-style questions focusing on reading coordinates from a grid.
Edexcel
The point A is shown on the coordinate grid.
Which number is the x-coordinate of point A?
Edexcel
The point A is shown on the coordinate grid.
Which number is the y-coordinate of point A?
AQA
Exam-style questions focusing on identifying quadrants.
AQA
The point (4, -3) is shown on the grid.
In which quadrant is the point?
AQA
Plot the point (-5, 2).
Which quadrant is this point in?
OCR
Exam-style questions focusing on reasoning with coordinates and movement.
OCR
The point (0, 4) lies on the coordinate grid.
Explain why this point is not in any quadrant.
OCR
A point moves from (-2, 1) to (3, -2).
Describe the movement.
Exam Checklist
Step 1
Check that you are reading the coordinate as \((x,y)\).
Step 2
Move horizontally first, then vertically.
Step 3
Watch carefully for negative numbers.
Step 4
Use the signs of x and y to identify the correct quadrant.
Most common exam mistakes
Wrong order
Reading \((x,y)\) as \((y,x)\).
Wrong direction
Going right instead of left, or up instead of down.
Quadrant confusion
Forgetting the sign pattern in each quadrant.
Axis points
Points on the axes are not inside a quadrant.
Common Mistakes
These are common mistakes students make when working with coordinates in GCSE Maths.
Writing coordinates in the wrong order
Incorrect
A student writes a point as (y, x) instead of (x, y).
Correct
Coordinates are always written in the order (x, y), where x is the horizontal movement and y is the vertical movement.
Moving vertically before horizontally
Incorrect
A student moves up or down first when plotting a point.
Correct
Always move horizontally first (x-direction), then vertically (y-direction) when plotting coordinates.
Misunderstanding negative x-values
Incorrect
A student moves right when the x-value is negative.
Correct
Negative x-values mean move to the left on the coordinate grid, while positive x-values move to the right.
Misunderstanding negative y-values
Incorrect
A student moves up when the y-value is negative.
Correct
Negative y-values mean move down the grid, while positive y-values move upwards.
Mixing up the quadrants
Incorrect
A student places a point in the wrong quadrant.
Correct
Each quadrant has a specific sign pattern: (+,+), (-,+), (-,-), (+,-). Use this to check the correct position of a point.
Try It Yourself
Practise plotting and interpreting coordinates on the Cartesian plane.
Foundation
Foundation Practice
Read and plot coordinates, identify quadrants and interpret simple movements.
Which quadrant is point (-3, 4) in?
Negative x, positive y.
That is Quadrant II.
Write the coordinates of point B.
Left is negative, down is negative.
2 left and 2 down → (-2, -2).
Which point lies on the y-axis?
x = 0 on y-axis.
Points on the y-axis have x = 0.
Move point (2, 3) 3 units right. What are the new coordinates?
Increase x only.
(2 + 3, 3) = (5, 3).
Which quadrant is (4, -2) in?
Positive x, negative y.
That is Quadrant IV.
Write the coordinates of the origin.
Where axes meet.
The origin is (0, 0).
Which point is 3 units above (1, 2)?
Change y only.
(1, 2 + 3) = (1, 5).
Move (-2, -3) 4 units up. Find the new coordinates.
Increase y.
-3 + 4 = 1 → (-2, 1).
Which coordinate is in Quadrant I?
Both positive.
Quadrant I has positive x and y.
Higher
Higher Practice
Work with midpoints, distances and coordinate geometry reasoning.
Find the midpoint of (2, 4) and (6, 8).
Average x and y.
(2+6)/2 = 4 and (4+8)/2 = 6.
Which formula finds the midpoint?
Average coordinates.
Midpoint is the average of x and y values.
Find the midpoint of (-2, 3) and (4, 7).
Average values.
(−2+4)/2 = 1 and (3+7)/2 = 5.
Find the distance between (0, 0) and (3, 4).
Use Pythagoras.
√(3² + 4²) = 5.
What is the distance between (1,1) and (1,6)?
Vertical distance.
6 − 1 = 5.
Find the distance between (2,3) and (5,7).
Use Pythagoras.
√((5−2)² + (7−3)²) = √(9+16) = 5.
Which pair forms a horizontal line?
Same y value.
Horizontal lines have equal y-values.
Find the midpoint of (1, 2) and (7, 6).
Average coordinates.
(1+7)/2 = 4 and (2+6)/2 = 4.
Which pair forms a vertical line?
Same x value.
Vertical lines have equal x-values.
Find the midpoint of (-4, 2) and (2, 6).
Average both coordinates.
(-4+2)/2 = -1 and (2+6)/2 = 4.
Games
Practise this topic with interactive games.
Games coming soon.
Frequently Asked Questions
What are coordinates?
Points on a grid given as (x, y).
What is the origin?
(0,0) on the grid.
How do I plot points?
Move along x-axis first, then up or down y-axis.