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This coordinate-geometry topic finds the distance between two points using Pythagoras and the midpoint by averaging coordinates — the starting point for straight lines and circles. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Distance is the square root of the squared differences added together — square the differences before adding, not after. The midpoint is the mean of the x values and the mean of the y values.
Before you start
This builds directly on coordinates and Pythagoras. This sits in Pure 1. It then feeds into straight lines and circles.
What you learn
Two formulas — but they do far more than measure. With them you can prove a triangle is right-angled, find a missing coordinate, locate the fourth corner of a parallelogram, and pin down the centre and radius of a circle. Leave your answer as an exact surd unless told otherwise. The distance formula does not just measure — it proves. Turn the words into an equation, then solve it. The course works through the distance between two points, the midpoint, proving properties of shapes, finding unknown coordinates and putting it together. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
In our A-level maths courses, Distance & Midpoint belongs to Coordinate Geometry and is met in the AS year. There are 5 teaching sections and 5 fully worked examples, plus 5 sets of check questions. Related topics students usually take next include Parametric Equations, Straight Lines, Circles — Equation & Properties and Circles — Tangents & Chords. You can drill this strand further on the Coordinate Geometry revision engine, with your accuracy saved to your skill tree.
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