Position and Location in Three Dimensions — AC9M8SP03

• Interpret ordered triples in a defined 3D coordinate system.
• Compare 2D and 3D descriptions of position.
• Use layers, plan/elevation views and digital models to locate objects.
• Explain how origin, axis direction and scale affect coordinates.

Recall the Cartesian plane, ordered pairs, coordinates, origin, positive/negative directions, scale, plan view and simple 3D objects.

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.

• 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.

1. Plot or describe A(2,3,4) from a stated origin.
2. Compare A(2,3,4) and B(2,3,9) in plan view.
3. Translate a multi-storey car-park location such as bay (5,8) on level 3 into a three-coordinate description.
4. Explain one similarity and one difference between 2D and 3D coordinate systems.

1. Interpret P(−1,4,2).
2. Give two points sharing the same xy plan location but different heights.
3. Describe how changing the origin changes coordinates without moving the object.
4. List the 8 vertices of a unit cube in the first octant.
5. Compare a virtual map view with a street/elevation view of the same object.
6. Explain how a 3D printer uses coordinate information.
7. Design a 3D noughts-and-crosses coordinate convention and locate three cells.

Two teams describe the same drone location using different origins and axis directions, so their coordinate triples differ. Explain how both descriptions can be correct and what information must be shared before coordinates can be compared safely.

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.

1. Points A(2,5,1) and B(2,5,7) are shown in plan view. Explain why they appear at the same location and what information distinguishes them.
   Identify the omitted coordinate in the projection.
2. A cuboid has one vertex at (0,0,0) and opposite vertex at (4,3,2). List all vertices.
   Each coordinate independently takes its minimum or maximum value.
3. A coordinate system’s origin is moved 3 units in the +x direction. Explain how x-coordinates of fixed objects change.
   Coordinates are relative to the new origin; the objects do not move.

• I interpret ordered triples.
• I compare 2D and 3D views.
• I define origin, axes and scale.
• I connect coordinates to real/digital 3D contexts.

Exit ticket: How can two distinct 3D points appear at one point in a 2D plan view?

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.

• AC9M8A02 — Cartesian plane and linear relations
• AC9M8SP04 — geometric algorithms

• Australian Curriculum v9.0
• Victorian Curriculum F–10 Version 2.0 Mathematics
• NSW Mathematics K–10 Syllabus (2022)

Curriculum equivalents for The position and location of objects in 3 dimensions in...

Mapped skill: describe the position and location of objects in 3 dimensions in different ways, including using a three-dimensional coordinate system with the use of dynamic geometric software and other digital tools

These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.

Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.