Coordinates (Edexcel GCSE Maths): Revision Notes
Coordinates
What are coordinates?
Coordinates are pairs of numbers that tell us exactly where points are positioned on a grid. Think of them like a postal address for points - they give us precise instructions for finding any location on the coordinate plane.
The coordinate system is fundamental to mathematics, from basic graphing to advanced calculus. Understanding coordinates helps us describe positions, distances, and relationships between points in space.
The coordinate system uses two perpendicular lines called axes to create a reference framework:
- The horizontal axis is called the x-axis
- The vertical axis is called the y-axis
- These axes meet at a special point called the origin, which has coordinates (0, 0)
Reading and writing coordinates
Every coordinate is written as a pair of numbers in brackets, like this: (x, y)
The first number (x-coordinate) tells us:
- How far to move horizontally from the origin
- Positive numbers mean move right
- Negative numbers mean move left
The second number (y-coordinate) tells us:
- How far to move vertically from the origin
- Positive numbers mean move up
- Negative numbers mean move down
Remember: Think "along the corridor, then up the stairs" - always go horizontally first, then vertically. This is the most common mistake students make when reading coordinates!
Plotting points on a grid
To plot a point with coordinates (a, b):
- Start at the origin (0, 0)
- Move 'a' units horizontally (right if positive, left if negative)
- Move 'b' units vertically (up if positive, down if negative)
- Mark the point with a cross (×)
Worked Example: Plotting a Point
To plot the point (3, 2):
- Move 3 units right from the origin
- Move 2 units up
- Mark the point with a cross (×)
The point (3, 2) will be located 3 squares to the right and 2 squares up from where the axes meet.
Mid-points of line segments
A line segment is a straight line connecting two points. The mid-point is the point that sits exactly halfway between the two endpoints.
Mid-points are essential in geometry for finding centres of shapes, creating perpendicular bisectors, and solving many geometric problems involving symmetry and balance.
To find the mid-point between two points, you need to:
- Add the x-coordinates of both endpoints and divide by 2
- Add the y-coordinates of both endpoints and divide by 2
Mid-point formula
If you have two points and , the mid-point is:
Worked Example: Finding a Mid-point
Find the mid-point between (4, 1) and (12, 5):
Step 1: Find the x-coordinate of the mid-point
Step 2: Find the y-coordinate of the mid-point
Step 3: Write the final answer The mid-point is at (8, 3)
Exam tips
Essential Exam Strategies
- Always check you've read coordinates in the correct order (x, y)
- When plotting points, use a sharp pencil and mark clearly with crosses
- For rectangle problems, remember that opposite corners will have some coordinates the same
- Mid-point questions often appear in higher grade questions, so practice the formula
- Double-check negative coordinates - they're easy to mix up in exams
Key Points to Remember:
- Coordinates describe exact positions on a grid using two numbers (x, y)
- The x-coordinate tells you horizontal position, the y-coordinate tells you vertical position
- The origin (0, 0) is where the x-axis and y-axis meet
- Mid-points are found by averaging the coordinates of the endpoints using the formula
- Always read coordinates as "across first, then up" - never the other way around