7.4 Grid References, Coordinates, GPS Data, Compass Directions, and Bearings

Alphanumeric Grid References and Cartesian Coordinates

School campus maps, excursion street directories, and orienteering courses rely on two main coordinate systems. Both follow the universal convention of reading horizontal position first, then vertical position second ("along the corridor, then up or down the stairs"):

1. Alphanumeric Grid References (Area Grids): Columns are labelled with letters (A, B, C, ...) across the top or bottom, and rows are labelled with numbers (1, 2, 3, ...) along the side. A reference such as C4 designates the entire grid square where column C intersects row 4.
2. Cartesian Coordinates $(x, y)$ and Topographic Grid Lines (Point Grids): Grid lines themselves are numbered from an origin $(0, 0)$. In $(x, y)$, the first number $x$ is the horizontal displacement along the $x$-axis (eastings on a topographic map, increasing from West to East), and the second number $y$ is the vertical displacement along the $y$-axis (northings, increasing from South to North).

When navigating between two grid points $(x_1, y_1)$ and $(x_2, y_2)$ on a rectangular street or corridor layout, distinguish between two distance measures:

• Grid (walking) distance along perpendicular paths: $|x_2 - x_1| + |y_2 - y_1|$ grid units.
• Direct (straight-line / "as the crow flies") distance: always shorter than the grid distance when both coordinates change. Calculating it requires Pythagoras' theorem, which ACER's framework treats as out-of-scope technical content, so LANTITE items give this distance or ask you to measure it against a scale bar.

Worked Example 1: Navigating an Alphanumeric Campus Grid

A school map is divided into square grid cells of side length $40\text{ m}$, with columns A to H running from West to East and rows 1 to 6 running from North to South (so row 1 is along the northern boundary). A student walks from the centre of cell B2 to the centre of cell F5 following horizontal and vertical pathways. In which compass directions and how far does the student walk?

1. Horizontal movement (Column B to Column F): Moving from the $2\text{nd}$ column (B) to the $6\text{th}$ column (F) is $6 - 2 = 4$ grid columns East, covering $4 \times 40\text{ m} = 160\text{ m}$ East.
2. Vertical movement (Row 2 to Row 5): Because row numbers increase from North to South on this directory grid, moving from row 2 to row 5 is $5 - 2 = 3$ grid rows South, covering $3 \times 40\text{ m} = 120\text{ m}$ South.
3. Total walking distance: $160\text{ m} + 120\text{ m} = 280\text{ m}$. The straight-line distance between the two cell centres is shorter, but a question about following the pathways asks for the distance actually walked.

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The 8-Point Compass Rose and True Bearings

The 8-point compass rose consists of four cardinal directions (N, E, S, W) separated by $90^\circ$, and four intercardinal (ordinal) directions (NE, SE, SW, NW) positioned halfway ($45^\circ$) between adjacent cardinal points.

A three-figure true bearing expresses any horizontal direction as an angle from $000^\circ$ to $360^\circ$ measured using three strict rules:

1. Start facing True North ($000^\circ$).
2. Turn clockwise through the required angle.
3. Write the angle with three digits, using leading zeros for angles under $100^\circ$ (e.g., $045^\circ$, $008^\circ$).

To convert a compass quadrant bearing (such as $\text{S } 30^\circ\text{ E}$ or "$25^\circ$ West of North") into a three-figure true bearing, start from the named North or South pole ($000^\circ/360^\circ$ for North, or $180^\circ$ for South) and add or subtract the acute angle toward East or West:

• $\text{N } 35^\circ\text{ E}$ ($35^\circ$ East of North): $000^\circ + 35^\circ = 035^\circ$.
• $\text{S } 30^\circ\text{ E}$ ($30^\circ$ East of South): $180^\circ - 30^\circ = 150^\circ$.
• $\text{S } 40^\circ\text{ W}$ ($40^\circ$ West of South): $180^\circ + 40^\circ = 220^\circ$.
• $\text{N } 25^\circ\text{ W}$ ($25^\circ$ West of North): $360^\circ - 25^\circ = 335^\circ$.

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Reverse Bearings: Finding the Return Direction

Pay close attention to the word "from" in bearing questions:

• "The bearing of B from A" means A is your starting observation point. Draw a North line at A and measure clockwise to the line pointing toward B.
• "The bearing of A from B" is the reverse (or back) bearing—the direction you must travel to return from B back to A, which differs by a half-turn ($180^\circ$):

$$\text{Reverse Bearing} = \begin{cases} \theta + 180^\circ & \text{if } \theta < 180^\circ \\ \theta - 180^\circ & \text{if } \theta \ge 180^\circ \end{cases}$$

On the 8-point compass, you find the reverse direction instantly by swapping North $\leftrightarrow$ South and East $\leftrightarrow$ West:

• If the sports oval is North-West ($315^\circ$) from the library, then the library is South-East ($315^\circ - 180^\circ = 135^\circ$) from the sports oval.

Worked Example 2: Forward and Reverse True Bearings

On an orienteering course, Checkpoint 2 is on a true bearing of $068^\circ$ from Checkpoint 1. What is the true bearing of Checkpoint 1 from Checkpoint 2?

1. The forward bearing from Checkpoint 1 to Checkpoint 2 is $\theta = 068^\circ$.
2. Because $068^\circ < 180^\circ$, add $180^\circ$ to find the return bearing:

$$\theta_{\text{reverse}} = 068^\circ + 180^\circ = 248^\circ$$

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Multi-Step Navigation: Absolute Directions vs. Relative Turns

Campus map questions frequently combine absolute compass directions (which always refer to North, South, East, and West on the map) with relative egocentric turns (which depend on the direction the person is currently facing):

• Turning right ($90^\circ$ clockwise): Add $90^\circ$ to your current bearing.
• Turning left ($90^\circ$ anticlockwise): Subtract $90^\circ$ from your current bearing.
• Turning $45^\circ$ right or left: Step one position clockwise or anticlockwise on the 8-point compass rose.

The South-Facing Left/Right Trap: When a student walks South (down the page on a standard North-up map), their left-hand side is toward the East (the right side of the printed page) and their right-hand side is toward the West (the left side of the printed page). Always track the walker's current compass heading at each step rather than relying on left/right of the screen.

Worked Example 3: Tracking Relative Turns and Final Displacement

A teacher leaves the main office facing East, walks $120\text{ m}$ straight ahead, turns $90^\circ$ clockwise (right) and walks $90\text{ m}$, then turns $90^\circ$ anticlockwise (left) and walks $40\text{ m}$ to the science block. What direction is the teacher facing upon arrival, and how far East and South of the main office is the science block?

1. Leg 1: Walks $120\text{ m}$ East ($090^\circ$).
2. Leg 2: From facing East ($090^\circ$), a $90^\circ$ clockwise turn faces South ($090^\circ + 90^\circ = 180^\circ$). Walks $90\text{ m}$ South.
3. Leg 3: From facing South ($180^\circ$), a $90^\circ$ anticlockwise (left) turn faces East ($180^\circ - 90^\circ = 090^\circ$). Walks $40\text{ m}$ East.
4. Final position and heading: The teacher arrives facing East, located $120\text{ m} + 40\text{ m} = 160\text{ m}$ East and $90\text{ m}$ South of the main office.

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Reading GPS Data: Coordinates, Track Logs, and Elevation

ACER's framework lists GPS data alongside maps, plans, scales, and bearings. On the test, GPS data appears as numbers to read and compare, not as navigation theory.

GPS Coordinates (Latitude and Longitude)

A GPS position is a pair of angles, usually written in decimal degrees:

• Latitude measures north–south position from the equator ($0^\circ$). Australia lies in the Southern Hemisphere, so its latitudes are written as negative numbers or with an S: Darwin is about $-12.5^\circ$ ($12.5^\circ\text{S}$) and Hobart about $-42.9^\circ$. A more negative latitude is further south.
• Longitude measures east–west position from the prime meridian through Greenwich. All of Australia has east (positive) longitudes, from about $113^\circ\text{E}$ on the Western Australian coast to about $153.6^\circ\text{E}$ at Cape Byron, so a larger longitude is further east.

Each degree of latitude spans roughly $111\text{ km}$ of north–south distance, so a latitude difference of $0.01^\circ$ is about $1.1\text{ km}$.

GPS Track Logs from Fitness Apps and Watches

Excursion and sport questions often show a table exported from a GPS device. Treat it like a timetable with a cumulative distance column:

• Segment distance is the difference between cumulative readings: from 09:12 to 09:30 the group covered $4.5 - 2.1 = 2.4\text{ km}$.
• Segment speed is segment distance divided by segment time in hours: $18\text{ minutes} = 0.3\text{ hours}$, so the speed is $2.4 \div 0.3 = 8\text{ km/h}$.
• Pace (minutes per kilometre), as many running apps report it: $41\text{ minutes} \div 6.0\text{ km} \approx 6.83\text{ min/km}$, or about $6\text{ minutes }50\text{ seconds}$ per kilometre.
• Elevation: total climb adds every rise ($16 + 39 = 55\text{ m}$), whereas net change compares only the start and finish ($61 - 42 = 19\text{ m}$). Read the question to see which one it wants.

GPS distances are measured along the route actually travelled, so a GPS log usually shows a longer distance than a straight line drawn between the start and finish on a map.