GCSEMathsEdexcelHigherRevision Notes2. AlgebraCoordinate GeometryLength of a Line

Length of a Line (Edexcel GCSE Maths)

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Jamie Wood

Written by: Jamie Wood

Reviewed by: Dan Finlay

Length of a Line

How do I calculate the length of a line?

  • The distance between two points with coordinates open parentheses x subscript 1 space comma space y subscript 1 close parentheses and open parentheses x subscript 2 space comma space y subscript 2 close parentheses can be found using the formula

d equals square root of open parentheses x subscript 1 minus x subscript 2 close parentheses squared plus open parentheses y subscript 1 minus y subscript 2 close parentheses squared end root

  • This formula uses Pythagoras’ theorem  a squared plus b squared equals c squared

    • It is applied to the difference in the x-coordinates and the difference in the y-coordinates

A right-angled triangle drawn between two point on a straight line, to show how Pythagoras is used to find the length of a line

Examiner Tips and Tricks

  • Be extra careful when negative coordinates are involved

    • It can help to put negative numbers in brackets to make your working clearer

    • E.g. open parentheses negative 6 close parentheses minus open parentheses negative 8 close parentheses equals 2

Worked Example

Point A has coordinates (3, -4) and point B has coordinates (-5, 2).

Calculate the distance of the line segment AB.

Using the formula for the distance between two points, d equals square root of open parentheses x subscript 1 minus x subscript 2 close parentheses squared plus open parentheses y subscript 1 minus y subscript 2 close parentheses squared end root 

Substitute in the two given coordinates

d equals square root of open parentheses 3 minus open parentheses negative 5 close parentheses close parentheses squared plus open parentheses open parentheses negative 4 close parentheses minus 2 close parentheses squared end root

Be careful with the negative numbers
3 minus open parentheses negative 5 close parentheses equals 8 and open parentheses negative 4 close parentheses minus 2 equals negative 6

Simplify

d equals square root of open parentheses 8 close parentheses squared plus open parentheses negative 6 close parentheses squared end root space equals space square root of 64 plus 36 end root equals square root of 100 equals 10

10 units

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    Author
    Reviewer
    Jamie Wood

    Author: Jamie Wood

    Expertise: Maths

    Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths 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.