Coordinates (AQA GCSE Maths): Revision Notes
Coordinates
What are coordinates?
Coordinates are pairs of numbers that tell you exactly where a point is positioned on a grid. They work like a postal address for mathematical points - giving you precise directions to find any location on a coordinate plane.
The coordinate system uses two perpendicular lines called axes that cross at a central point called the origin.
Think of coordinates like giving someone directions to your house - you need both a street address and a house number to find the exact location!
Understanding the coordinate system
The coordinate system has two main parts:
- x-axis: The horizontal line running left to right
- y-axis: The vertical line running up and down
- Origin: The point where the axes cross, which has coordinates (0, 0)
Remember the phrase: "Along the corridor, then up the stairs" - this helps you remember that x-coordinates (horizontal) always come first, then y-coordinates (vertical).
How to read coordinates
Coordinates are always written in brackets as a pair: (x, y)
- The first number (x) tells you the horizontal position - how far left or right from the origin
- The second number (y) tells you the vertical position - how far up or down from the origin
Using negative coordinates
You can use negative numbers in coordinates:
- Negative x values: Points to the left of the origin
- Negative y values: Points below the origin
Example: Reading Negative Coordinates
The point (-4, -1) means:
- Move 4 units to the left of the origin (negative x)
- Move 1 unit down from the origin (negative y)
Working with shapes on coordinate planes
You can plot shapes like rectangles by placing their corners at specific coordinate points. This helps you calculate distances, areas, and other properties.
When plotting rectangles on coordinate planes, opposite corners will have some coordinates that match (either x or y values) because the sides are parallel to the axes.
Midpoints
A midpoint is the exact halfway point between two coordinates on a line segment. To find the midpoint when you know the coordinates of both ends, you can use the midpoint formula.
Midpoint formula
The Midpoint Formula:
This means:
- Add the two x-coordinates together and divide by 2
- Add the two y-coordinates together and divide by 2
- Write your answer as a coordinate pair
Example midpoint calculation
Worked Example: Finding a Midpoint
To find the midpoint between (4, 1) and (12, 5):
Step 1: Find the x-coordinate of the midpoint
Step 2: Find the y-coordinate of the midpoint
Step 3: Write as a coordinate pair Midpoint = (8, 3)
Exam tips
Essential Exam Strategies:
- Always write coordinates in brackets with the x-value first
- Check your signs carefully - negative coordinates can be tricky
- When finding midpoints, double-check your arithmetic
- For rectangle problems, remember that opposite sides are parallel and equal
- Practice plotting points to build confidence with the coordinate system
Key Points to Remember:
- Coordinates use the format (x, y) - horizontal position first, then vertical position
- The origin (0, 0) is where the x and y axes cross
- Negative coordinates place points left of or below the origin
- Midpoints are found by averaging the x-coordinates and y-coordinates separately
- Always check your signs when working with negative coordinates