Axes and coordinates

Part of MathsGraphs

Key points

A graph showing the x axis and y axis increasing in units of one from zero to eight, intersecting with each other at zero comma zero. An orange arrow is pointing to the intersecting point which is labelled with open brackets zero comma zero closed brackets.
The origin is the position where 𝒙 and π’š are both zero. It has the coordinates (0, 0).

  • A graph is drawn on a pair of . The 𝒙- is horizontal and the π’š- is vertical. The point at which the axes meet is called the .

  • Axes are labelled with numbers, in equal steps, which are placed in line with the gridlines. The on the axes do not need to be the same.

  • Ordered pairs called are used to fix a position on a graph. A point is plotted using coordinates in the form (𝒙, π’š).

  • The 𝒙 value gives the movement from the origin along the 𝒙-axis and the π’š value gives the movement from the origin along the π’š-axis.

A graph showing the x axis and y axis increasing in units of one from zero to eight, intersecting with each other at zero comma zero. An orange arrow is pointing to the intersecting point which is labelled with open brackets zero comma zero closed brackets.
The origin is the position where 𝒙 and π’š are both zero. It has the coordinates (0, 0).
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Understanding axes

For a simple graph, the is used. A graph has two axes that form an L-shape. The axes are labelled 𝒙 and π’š.

  • The 𝒙-axis is the horizontal line and the π’š-axis is the vertical line.

  • The origin is the position where 𝒙 = 0 and π’š = 0. The origin has coordinates (0, 0).

To draw axes for a given set of coordinates:

  • The axes will include all given coordinate values of 𝒙 and π’š.

  • The scales used depends on the values of 𝒙 and π’š, and on the available grid.

    • If possible, use a scale counting in ones.
    • For larger values, use larger steps. Eg, count in 2, 4, 5, 10, 20, 50, 100
    • For smaller values, use smaller steps. Eg, count in 0Ϋ°1, 0Ϋ°2, 0Ϋ°5
    • Avoid steps counting in numbers which are difficult to subdivide, such as 3, 6 or 7

  • Remember that the scales on each axis do not have to be the same. The 𝒙-axis could be labelled in steps of 5 and the π’š-axis in steps of 20

Examples

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  1. A graph showing the x axis and y axis increasing in units of one from zero to eight, intersecting with each other at zero comma zero.

    A pair of axes, labelled 𝒙 and π’š.

Question

A graph on the left labelled A and a graph on the right labelled B. Graph A on the left is showing the x axis increasing in units of five from zero to twenty and the y axis increasing in units of twenty up to one hundred and twenty. They intersect at zero comma zero. Graph B on the right is showing the x axis increasing in units of five up to twenty and the y axis increasing in tens up to sixty. They intersect at zero comma zero.

Decide which grid, A or B, is most suitable for plotting points where the maximum coordinate for 𝒙 is 17 and the maximum coordinate for π’š is 59

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Understanding and plotting coordinates in the first quadrant

The uses positive values for the 𝒙-axis and the π’š-axis. The axes form an L -shape.

Coordinates are ordered pairs of 𝒙 and π’š.

  • The (𝒙, π’š) gives a position on a coordinate grid.
  • The first coordinate value represents 𝒙. This is a horizontal movement to the right from the origin.
  • The second coordinate value represents π’š. This is a vertical movement up from the origin.
  • The combined movements of 𝒙 and π’š give the position of the plotted point.

Examples

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  1. A graph showing the x axis and y axis increasing in units of one from zero to six, intersecting with each other at zero comma zero. A point four units across the x axis and one unit up the y axis is labelled open brackets four comma one close brackets. At the right of the graph, the graph is labelled with open brackets x comma y closed brackets equals open brackets four comma one closed brackets.

    Coordinates are an ordered pair of 𝒙 and π’š which give a position on a grid.

Question

A graph showing the x axis and y axis increasing in units of one from zero to nine, intersecting with each other at zero comma zero. There are three points on the graph joined together with three lines to create a triangle shape – this is highlighted orange. The first point is plotted one unit across the x axis and two units up the y axis. A second point is plotted seven units across the axis and one unit up the y axis. A third point is plotted four units across the x axis and eight units up the y axis.

List the coordinates that create the triangle drawn on the grid.

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Practise axes and coordinates

Quiz

Practise reading axes and plotting coordinates with this quiz. You may need a pen and paper to help you with your answers.

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Real-life maths

Understanding coordinates is useful for map reading.

The location of a position on an Ordnance Survey (OS) map is managed by using a six-figure grid reference.

A graph showing the x axis increasing in units of one from eleven to fourteen and the y axis increasing in units of one from forty to forty three. The graph is divided into squares. One square is divided into an even smaller square, with the x axis and y axis increasing in units of one from zero to nine and intersecting at zero comma zero. One of the smaller squares is shaded blue with a black dot seven units across the x axis and two units up the y axis.

This works by first identifying an area using a four-figure grid reference. The square is then subdivided into a 10 by 10 grid for more precise detail.

Understanding grid references is useful when learning OS map skills.

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