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Midpoint of a Line (OCR GCSE Maths): Revision Note

Exam code: J560

Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

Updated on

OCR Maths: FoundationAQA Maths: FoundationOCR Maths: HigherAQA Maths: HigherEdexcel Maths: FoundationEdexcel Maths: HigherOCR Maths: FoundationAQA Maths: FoundationOCR Maths: HigherAQA Maths: HigherEdexcel Maths: FoundationEdexcel Maths: Higher

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 open parentheses x subscript 1 comma space y subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 close parentheses is

open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction space comma space fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction close parentheses

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 open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction space comma space fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction close parentheses

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

open parentheses fraction numerator negative 4 plus 8 over denominator 2 end fraction space comma space fraction numerator 3 plus negative 12 over denominator 2 end fraction close parentheses equals open parentheses 4 over 2 comma space fraction numerator negative 9 over denominator 2 end fraction close parentheses

Simplify

(2, −4.5)

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Author
Reviewer
Mark Curtis

Author: Mark Curtis

Expertise: Maths Content Creator

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.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.