Coordinate Geometry
Where algebra meets shape: plotting points, gradients, the equation of a line, parallel and perpendicular lines, and finding lengths and areas straight from coordinates.
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The Math Map
You have learned to manipulate algebra, draw graphs, and work with functions. Now let us place shapes on a grid and use algebra to measure them.
Imagine a giant grid covering the entire world, where every spot has its own unique address. Coordinate geometry is the bridge that turns shapes into numbers and equations into pictures.
Formula
In this topic you will find lengths, slopes, and the hidden relationships between lines just by reading their addresses.
Memory trick
Coordinates are just 'GPS for Shapes'!
What You Will Learn
You will start by reading a line off the grid, then learn to describe any line by its equation, and finish by answering questions about whole shapes using nothing but their addresses.
Steps
- 1
Coordinates and plotting points, then the gradient of a straight line.
- 2
The forms y = mx + c and ax + by + c = 0, and reading an equation off a graph.
- 3
Finding the equation of the line through two given points.
- 4
Parallel lines, perpendicular lines, and the perpendicular bisector.
- 5
Length of a line segment, area from coordinates, and the geometry of shapes on a grid.
Formula
The workhorse — the gradient of a line:
Every question about steepness, parallels and perpendiculars begins here.
Practise coordinate geometry now
Interactive visual aids, then real past-paper questions marked on your working like the exam. Free to start.
Practise free on LemmaraLemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education or Pearson Edexcel. The lessons and worked examples are Lemmara’s own.