GCSEMathsWJECMaths & Numeracy (Double Award)HigherRevision NotesAlgebraCoordinate Geometry & Linear GraphsCoordinates using Distance & Angle

Coordinates using Distance & Angle (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Exam code: 3320

Jamie Wood

Written by: Jamie Wood

Reviewed by: Mark Curtis

Updated on

Coordinates using Distance & Angle

How do I find a coordinate using a distance and angle?

  • You may be told a distance and an angle from a known coordinate to another unknown coordinate

    • In an exam question, the angles could be

      • written as bearings from north

      • labelled on a diagram

      • described relative to a given line e.g. to y equals 4 or to a line segment A B

  • Start by drawing a diagram, or annotating a given diagram

  • If the given angle is a multiple of 90 you can find the unknown coordinate just using addition or subtraction

    • Add or subtract the given distance from the x or y coordinate

    • Drawing a diagram will help you to spot how to find the unknown coordinate

  • The diagram below shows how to find the coordinates a distance of 5 from the point (1, 4) at angles 90°, 180°, 270°, and 360° (or 0°) from North

Coordinate grid with a central point at (1, 4) and four surrounding points: (1, 9), (6, 4), (-4, 4), and (1, -1), marked by crosses.

Worked Example

The point A has coordinates (2, 3).

The point P has coordinates (5, 3).

Point B is 5 units away from A at an angle of 270° measured anticlockwise from the line A P.

Determine the coordinates of B.

Answer:

Draw a diagram showing the points A and P, noting that their relative positions

Join them to form the line A P

Line segment between points A (2, 3) and P (5, 3) with crosses at each end, indicating a horizontal line on a coordinate plane.

Point B is 270° (three-quarters of a full turn) from the line A P, measured anticlockwise

The distance along this direction is 5 units

Diagram with points A(2,3) and P(5,3), a 270° angle at A with an arc, line AB measures 5 units vertically, and AP is horizontal.

You can now spot that B is 5 units directly below A

Subtract 5 from the y coordinate of A

open parentheses 2 comma space 3 minus 5 close parentheses

B is (2, -2)

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    Author
    Reviewer
    Jamie Wood

    Author: Jamie Wood

    Expertise: Maths Content Creator

    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.

    Mark Curtis

    Reviewer: 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.