International ASMathsEdexcelPure 1Revision NotesCoordinate Geometry in the (x, y) PlaneEquation of a Straight LineBasic Coordinate Geometry

Basic Coordinate Geometry (Edexcel International AS Maths: Pure 1): Revision Note

Exam code: XMA01

Written by: Paul

Reviewed by: Dan Finlay

Updated on 2 July 2026

Basic coordinate geometry

What is basic coordinate geometry?

Basic coordinate geometry refers to working with points, lines and shapes on the coordinate axis
Cartesian coordinates are simply the x -y coordinate system
Using coordinates you can
- Calculate the distance between two points (length of a line)
- Divide lines in m:n ratio,
- Find the mid-point of a line
- Calculate the area of a triangle (or other shapes)
- Find missing coordinates using any of the above
Most of these involve working with straight line graphs
Straight line graphs are of the form y = mx + c
- m is the gradient
- c is the y-axis intercept
- Part of a straight line is called a line segment

Basic Coordinate Geometry Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

How do I find the length of a line segment?

By finding the distance, d, between two points (x₁, y₁) and (x₂, y₂)
Pythagoras’ Theorem (a² = b² + c²) is used to find the length of a line

Basic Coordinate Geometry Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

Basic Coordinate Geometry Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes

Basic Coordinate Geometry Notes Diagram 4, A Level & AS Level Pure Maths Revision Notes

How do I find the midpoint of a line segment?

Basic Coordinate Geometry Notes Diagram 5, A Level & AS Level Pure Maths Revision Notes

M is often used as the midpoint between two points (x₁, y₁) and (x₂, y₂)
It is the average of both the x and y coordinates

Examiner Tips and Tricks

Work with the square of a distance for as long as possible as this avoids early rounding errors and surds.
Only square root when forced to or for a final answer, and use the ANS button (and other memory features) on your calculator.

How do I find the gradient of a line segment?

There are lots of ways to find the gradient, m, of a line segment

Use the two end points to find the change in y divided by change in x

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Equation of a Straight Line Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes

Worked Example

Basic Coordinate Geometry Example Diagram, A Level & AS Level Pure Maths Revision Notes

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