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National 5 Maths
3D Coordinates

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Page sections

Topic content

  • Determining coordinates of a point from a diagram representing a three-dimensional object

Textbook page numbers

  • Zeta National 5+ Maths p.285 Q17
  • TeeJay Maths Book N5 p.215 Q3
  • Leckie National 5 Maths pp.319-321

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Zeta National 5+ Maths
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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.

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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.

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.

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.

Example 6 (non-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.

Buy N5 Maths practice papers

Zeta: Five Practice Papers   TOP CHOICE
CGP: N5 Maths Exam Practice 
Leckie: Revision and Practice 
Hodder: N5 Maths Practice Papers 

Past paper questions

• All past paper questions by topic
• 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)
• 2025 Paper 2 Q8(a)

Buy our favourite N5 textbook

Zeta National 5+ Maths
Clear and comprehensive.
Progressive exercises.
Includes answers.
Buy from Zeta Press 

3D coordinates worksheets

Maths Hunter worksheet
• Practice questions (no answers)
Larkhall Academy exercises
• Pages 25-27 Ex 6 (no answers)

Buy N5 Maths revision guides

How to Pass N5 Maths    TOP CHOICE
BrightRED: N5 Maths Study Guide 
CGP: N5 Maths Revision Guide 

Notes and videos

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

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