Watch out
Swapping y and z.
Scottish National 5 Mathematics
National 5 Maths 3D coordinates
Determine the coordinates of points from diagrams of three-dimensional objects.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Trace each point parallel to the labelled x, y and z directions.
- Be ready to work exactly without a calculator and show each mathematical step.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
3D coordinates is an assessed part of Scottish National 5 Mathematics in the geometry area. Determine the coordinates of points from diagrams of three-dimensional objects.
Trace each point parallel to the labelled x, y and z directions.
Read coordinates in x, y, z order.
Check the point lies on the expected face or edge.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Visual support
Two Pythagoras steps inside a cuboid
Key formulae and rules
- A 3D coordinate is written (x, y, z).
Check
Trace each coordinate parallel to its labelled axis and keep the order x, y, z.
Exam tip
Mark the diagram with the values you use, show the formula and finish with the correct length, area or volume units.
Worked examples
Worked example 1
3D coordinates worked example
A cuboid starts at O(0,0,0) and has side lengths 4, 3 and 5. State the opposite vertex.
- Move 4 in x, 3 in y and 5 in z.
Answer: (4, 3, 5)
Watch out
- Swapping y and z.
- Reading perspective length instead of the axis scale.