GCSEMathsAQARevision Notes2. AlgebraCoordinate GeometryCoordinates

Coordinates (AQA GCSE Maths)

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Daniel I

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2D Coordinates

What are 2D coordinates?

  • A graph in two dimensions is also known as a Cartesian plane
  • Normally the two dimensions are labelled x and y, where
    • the horizontal axis is x and the vertical axis is y
  • The two axes meet where x and y are both 0
    • This point, (0, 0), is known as the origin
  • The coordinate (x, y) tells us that the point is x units to the left/ right of the origin and y units below/ above the origin
    • If the x value is negative then the point is to the left of the origin, and if the x value is positive then the point is to the right of the origin
    • If the y value is negative then the point is below the origin, and if the y value is positive then the point is above the origin

Examiner Tip

  • "Along the corridor, up the stairs" is a useful way of remembering which way round (x, y) is
  • Pay close attention to the scale shown on the axes

Worked example

(a)
Write down the coordinates of the point A shown on the axes below. 
(b)
Mark the point B(3, -2) on the axes below.

2d-coordinates-we

(a)
A is 3 left of the origin so x = −3. And A is 4 above the origin so y = 4.
(−3, 4)

(b)
Starting at the origin, count 3 squares right and two squares down. Mark the point with a solid circle or a cross. 
6j_PGh2e_2d-coordinates-we-answer

3D Coordinates

What are 3D coordinates?

  • Some problems may contain three dimensions
  • Normally the three dimensions are labelled x, y, and z 
    • The z axis is perpendicular to x and y
  • If x is the length and y is the height, then z can be thought of as the depth
  • The coordinate point (x, y, z) is the distance from the origin along the x-axis, the distance from the origin along the y axis and the distance from the origin along the z axis

Examiner Tip

  • Be careful to write any 3D coordinates in the correct order of x, y, z

Worked example

A cuboid is shown on the 3D grid below.

3d-coordinates-we

P is a vertex of the cuboid.

Write the coordinates of P in the form open parentheses x comma space y comma space z close parentheses.

P is 6 along the x axis in a positive direction, 4 along the y axis in a positive direction, and 3 along the z axis in a positive direction.

Write these numbers in brackets, taking care to put them in the correct x, y, z order

stretchy left parenthesis 6 comma space 4 comma space 3 stretchy right parenthesis

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    Daniel I

    Author: Daniel I

    Expertise: Maths

    Daniel has taught maths for over 10 years in a variety of settings, covering GCSE, IGCSE, A-level and IB. The more he taught maths, the more he appreciated its beauty. He loves breaking tricky topics down into a way they can be easily understood by students, and creating resources that help to do this.