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Plotting coordinates in the four quadrants

Part of MathsGraphs

Key points

The four quadrants allow coordinates with negative and positive values to be plotted.
  • Understanding how to plot points in all four quadrants is essential for drawing linear (straight-line) graphs and quadratic graphs.
  • The \(x\) is , labelled with positive values to the right of the and negative values to the left of the origin.
  • The \(y\) is , labelled with positive values going up from the origin and negative values going down from the origin.
  • The axes at the origin (0, 0), dividing the into . Coordinates can be plotted using both positive and negative values.
The four quadrants allow coordinates with negative and positive values to be plotted.
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Understanding the four quadrants of a graph

  • When the \(x\)-axis and the \(y\)-axis intersect they create four quadrants. The point at which they cross is the origin. The \(x\)-axis is horizontal. The \(y\)-axis is vertical.

  • The are labelled with numbers regularly spaced from the origin, aligned with the gridlines. The on the axes do not need to be the same.

    • The \(x\)-axis is labelled with positive numbers increasing to the right and negative numbers decreasing to the left of the origin.
    • The \(y\)-axis is labelled with positive numbers increasing up and negative numbers decreasing down from the origin.

Understanding axes and coordinates is necessary when drawing and using axes in four quadrants. Inequality statements may be used to describe the range of values for each axis.

Examples

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

    When the horizontal 饾挋-补虫颈蝉 and the vertical 饾挌-补虫颈蝉 intersect, they create four quadrants.

Question

Minus three is equal to or less than x is equal to or less than five. Underneath: Minus four is equal to or less than y is equal to or less than two. Written below: X minimum minus three, maximum five. Y minimum minus four, maximum two.

Draw a pair of axes for the given \(x\) and \(y\) values.

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Plotting points in all four quadrants

The four quadrants allow with negative and positive values to be plotted.

  • The notation (\(x\), \(y\)) gives a position on a coordinate plane.
  • The first coordinate value represents \(x\). This is a horizontal movement from the origin.
  • The second coordinate value represents \(y\). This is a vertical movement from the origin.
  • The result of the \(x\) and \(y\) movements gives the position of the point that is plotted on the axes.

Example

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  1. A graph showing both the y axis and x axis going up in units of two from minus ten to ten 鈥 intersecting with each other at zero comma zero. In the top left a point is labelled open brackets minus seven comma five close brackets. In the top right a point is labelled open brackets eight comma nine close brackets. In the bottom left a point is labelled open brackets minus three comma minus six close brackets. In the bottom right a point is labelled open brackets six comma minus ten close brackets.

    The four quadrants allow coordinates with negative and positive values to be plotted.

Question

A graph showing the x axis and y axis increasing in units of one from minus four to four 鈥 intersecting with each other at zero comma zero. In the top left there is a point labelled A. In the bottom left there is a point labelled B. In the bottom right there is a point labelled C.

Which of the three points has the coordinates (3, -4)?

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Practise using the four quadrants

Quiz

Practise reading and plotting across the four quadrants. You may need a pen and paper to help you with your answers.

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Real-life maths

Archaeologists use grid referencing to map the location of discoveries when working on a site.

Archaeologists use coordinate grids to help them items and artefacts from the past and to locate important features.

A secure reference point is used as the origin (0, 0). A grid is measured out with string guidelines over the grid site to help map the location of items as they are found and excavated.

Setting up a grid system like this is essential to have accurate information during an archaeological dig.

Archaeologists use grid referencing to map the location of discoveries when working on a site.
A software engineer creating a 3D image using Computer Aided Design.

The \(x\) and \(y\) axes work on a two-dimensional (2D) plane. Coordinates in three-dimensional (3D) space are used in Computer-Aided Design (CAD) programs.

These allow users to create 3D images. CAD is used by game programmers, software engineers and in the development of film animation.

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Game - Divided Islands

Using your maths skills, help to build bridges and bring light back to the islands in this free game from 大象传媒 Bitesize.

Play the Divided Islands game!
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