Year 8 Mathematics · AC9M8SP03

Position and Location in Three Dimensions

A three-dimensional coordinate system needs three ordered coordinates referenced to a chosen origin and axes. Compare ordered triples, layers, plan/elevation views and…

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Key conceptTeach from the board

A point in a 3D Cartesian system is written as an ordered triple (x,y,z). The order matters. The third coordinate records position along a third axis, commonly height/depth.

Coordinates are meaningful only after the origin, axis directions and units are defined. The same physical location can have different coordinates if the reference system changes.

A plan view may hide height, while an elevation may hide depth. Layers can represent floors in a car park or levels in a game. Dynamic software lets students rotate a model and compare views without changing the underlying coordinates.

Preserve the full AC9 contexts: aircraft/drones using latitude–longitude–altitude, 3D printing/design software, virtual maps versus street views, first-octant constructions, multi-storey car parks, 3D noughts-and-crosses, and respectful exploration of geospatial technologies used by First Nations communities.

Worked examplesWe do

Worked examples

AC9M8SP03 - Position and Location in Three Dimensions
Example 1

Plot or describe A(2,3,4) from a stated origin.

Example 2

Compare A(2,3,4) and B(2,3,9) in plan view.

Example 3

Translate a multi-storey car-park location such as bay (5,8) on level 3 into a three-coordinate description.

Example 4

Explain one similarity and one difference between 2D and 3D coordinate systems.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M8SP03: describe position and location of objects in 3 dimensions in different ways, including a three-dimensional coordinate system and digital tools.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8SP03:Exact.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MAO-WM-01:Supporting. Current Stage 4 outcomes do not provide a direct three-dimensional Cartesian-coordinate counterpart; Working mathematically supports representation and reasoning without forcing a false geometry equivalence.

LessonAC v9VictoriaNSW
Position in 3DAC9M8SP03VC2M8SP03 — ExactMAO-WM-01 — Supporting
Questions and answersWith answers
  1. What does (x,y,z) represent? Position relative to three defined coordinate axes.
  2. Why can a plan view be ambiguous? Different z-values can project to the same x/y location.
  3. Why must the origin be stated? Coordinates are measured relative to it.
  4. What do digital 3D tools add? They allow construction, rotation and comparison of multiple representations of the same coordinate model.
Practice and reviewReady for practice
  • Ordered triples can be rearranged. Coordinate order is part of the definition.
  • Plan view shows full 3D position. It usually removes one dimension, often height.
  • Coordinates are absolute. They depend on the chosen origin, axes and scale.
  • A perspective sketch gives reliable coordinates. Perspective distorts apparent lengths/angles; use the coordinate/reference system.
Curriculum alignmentStart here
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