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3D coordinates

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3D coordinates help us locate points in three-dimensional space, just like GPS systems pinpoint locations in the real world. They're used in everything from video game design to architecture, allowing us to visualize and navigate spaces with height, width, and depth. Jump to the questions

Practise now

For each question, enter the coordinates of the red dot:

Topic guide

What this worksheet practises

This worksheet covers the concept of three-dimensional (3D) coordinates. While 2D coordinates use an x and y-axis to plot points on a flat plane, 3D coordinates add a z-axis to represent depth. This allows you to pinpoint locations in a three-dimensional space.

Key method

A 3D coordinate is written in the format (x, y, z).

  • The x-value tells you how far to move along the x-axis (usually left or right).
  • The y-value tells you how far to move along the y-axis (usually up or down, or forwards and backwards depending on the diagram's orientation).
  • The z-value tells you how far to move along the z-axis (representing the third dimension, often up or down from a flat plane).

To plot or read a coordinate, always start at the origin (0, 0, 0) and move along the axes in alphabetical order: x, then y, then z.

Worked example

Find the coordinate of the far top right corner of a cube if one corner is at the origin (0,0,0) and its side length is 5 units.

Step 1: Move 5 units along the x-axis. The position is now (5, 0, 0).

Step 2: Move 5 units along the y-axis. The position is now (5, 5, 0).

Step 3: Move 5 units up the z-axis. The final position is (5, 5, 5).

The coordinate is (5, 5, 5).

Useful tips

When working with cubes and cuboids on a 3D coordinate grid, remember that parallel edges have the same length. If you know the length of one side of a cuboid, you can use that distance to find the coordinates of other vertices without needing to count every single unit.

Things to remember

Always maintain the strict alphabetical order of (x, y, z) when reading and writing 3D coordinates. Mixing up the order is the most common reason for losing marks on these questions.