National 5 Maths
3D Coordinates
Course content
- Determining coordinates of a point from a diagram representing a three-dimensional object
Textbook page references
- Zeta National 5+ Maths
p.285 Q17 - TeeJay Maths Book N5 p.215 Q3
- Leckie National 5 Maths pp.319-321
Key ideas
- This short topic is closely related to vectors.
-
There is more than one way to represent 3D coordinates on a 2D piece of paper (or a webpage), but the most common orientation is:
- \(x\) on the page pointing, right →
- \(y\) going into the page ⬈
- \(z\) on the page, pointing up ↑
- Remember that (\(a\),\(b\),\(c\)) means the point that you arrive at if you start at the origin (0,0,0) and move \(a\) units in the direction of the \(x\)-axis, \(b\) units in the \(y\)-direction and \(c\) units in the \(z\)-direction.
N5 Maths revision course
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Example 1 (non-calculator)
The diagram shows a cuboid OABCDEFG, relative to the coordinate axes.
- OA = 8 units.
- OC = 5 units.
- OG = 6 units.
- M is the midpoint of DE.
- N is the point at the centre of the base.
(a) Write down the coordinates of A.
(b) Write down the coordinates of D.
(c) Write down the coordinates of E.
(d) Write down the coordinates of M.
(e) Write down the coordinates of N.
Recommended student book
Zeta Maths: National 5 Maths Textbook
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Example 2 (non-calculator)
The diagram shows a rectangular-based pyramid, relative to the coordinate axes.
The apex D is directly above the centre of the base.
The height of the pyramid equals the length of its base.
Write down the coordinates of D.
Example 3 (calculator)
SQA National 5 Maths 2014 P2 Q2
The diagram shows a cube placed on top of a cuboid, relative to the coordinate axes.
A is the point (8,4,6).
Write down the coordinates of B and C.
Recommended revision guides
How to Pass National 5 MathsBrightRED N5 Maths Study Guide
Example 4 (non-calculator)
SQA National 5 Maths 2017 P1 Q5
The diagram shows a square-based pyramid placed on top of a cube, relative to the coordinate axes.
The height of the pyramid is half of the height of the cube.
A is the point (6,0,0).
The point C is directly above the centre of the base.
Write down the coordinates of B and C.
Example 5 (non-calculator)
SQA National 5 Maths 2018 P1 Q13
The diagram shows a triangular prism, ABCDEF, relative to the coordinate axes.
• AD = AE.
• DC = 8 units.
• Edges EF, DC and AB are parallel to the y-axis.
Write down the coordinates of B and C.
N5 Maths practice papers
Non-calculator papers and solutionsCalculator papers and solutions
Example 6 (calculator)
SQA National 5 Maths 2019 P2 Q5
The diagram shows a cone with diameter 6 units and height 8 units.
• The \(x\)-axis and the \(y\)-axis are tangents to the base
• A is the point of contact between the base and the \(x\)-axis
• B is directly above the centre of the base
Write down the coordinates of A and B.
Example 7 (non-calculator)
SQA National 5 Maths 2021 P1 Q14(a)
The diagram shows a hemisphere relative to the coordinate axes.
• A is the point (6,0,0)
• C is the midpoint of diameter OA
• B is vertically below C
State the coordinates of B.
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Past paper questions
| • All past paper questions by topic |
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• 2014 Paper 2 Q2 • 2016 P1 Q7 (with 3D Pythagoras) • 2017 Paper 1 Q5 • 2018 Paper 1 Q13 • 2019 Paper 2 Q5 • 2021 Paper 1 Q14(a) |
Other great resources
| Video - Maths180.com |
| Video - Tynecastle Maths |
| Video - DLB Maths SQA 2014 Paper 2 Q2 solution |
| Notes and videos - Mistercorzi |
| Notes - BBC Bitesize Test yourself - BBC Bitesize |
| Lesson notes - Maths 777 |
| Practice questions - Maths Hunter |
| Exercises - Larkhall Academy Pages 25-27 Ex 6 |
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