IGCSEMathsEdexcelMaths A (Modular)Higher Unit 1Revision NotesGraphs & CoordinatesCoordinate GeometryMidpoint of a Line

Midpoint of a Line (Edexcel IGCSE Maths A (Modular))

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Author

Mark Curtis

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Maths

Midpoint of a Line

How do I find the midpoint of a line?

The midpoint of a line will be the same distance from both endpoints
You can think of a midpoint as being the average (mean) of two coordinates
The midpoint of $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is

$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Worked Example

The coordinates of A are (−4, 3) and the coordinates of B are (8, −12).

Find the coordinates of the midpoint of AB.

The midpoint can be found using $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Substitute in the values of x and y from each point into their correct positions

$(\frac{- 4 + 8}{2}, \frac{3 + - 12}{2}) = (\frac{4}{2}, \frac{- 9}{2})$

Simplify

(2, −4.5)

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Author: Mark Curtis

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.