# Compass Directions and Maps

> Use the eight compass points, follow a route on a grid with a scale, and read distances on a map.

From Selective School Maths on WhizzNotes, free study notes for NSW students: https://whizznotes.com/selective-school-maths/directions-and-maps/. Updated 3 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The treasure hunt
For his birthday, Theo's uncle hides a prize in the park and hands him a note:

"Start at the big gum tree. Walk 40 m north, 30 m east, then 10 m south. Dig under the bench."

Theo has a compass on his watch. He follows each step, turning to face the right way each time. In a few minutes he is standing at the bench, holding a box of chocolates.

Directions plus distances can describe any route. Maps use the same idea, with a **scale** to shrink real distances onto paper.

**In short:** The eight compass directions in clockwise order are N, NE, E, SE, S, SW, W and NW, each $45^\circ$ apart. On a map, the real distance is the map distance multiplied by the scale.

## Before you start

- Turning: a quarter turn is $90^\circ$, a half turn is $180^\circ$ (see Types of Angles).
- Multiplying by a scale, such as "1 cm stands for 10 m".

## The compass rose

*Diagram: Compass rose with north at the top, east on the right, south at the bottom and west on the left, plus north-east, south-east, south-west and north-west between them*
*Never Eat Soggy Weetbix: N, E, S, W going clockwise.*

### Key idea: Eight points
The four main points are **north, east, south, west**, going clockwise. Halfway between them are **north-east (NE), south-east (SE), south-west (SW)** and **north-west (NW)**.

On most maps north is at the top.

### Exam tip: Opposites
North and south are opposite. East and west are opposite. NE is opposite SW, and NW is opposite SE.

Each of the eight points is $45^\circ$ from its neighbour. Turning from north to east is $90^\circ$ clockwise.

## Describing where places are

"Sydney is east of Canberra" means if you stand in Canberra and face Sydney, you face east. Swap the places and the direction flips: Canberra is **west** of Sydney.

### Watch out: Read "from" carefully
"In which direction is Darwin **from** Broome?" means stand at Broome and look towards Darwin. Darwin is to the north-east of Broome. Broome is south-west of Darwin.

## Following a route on a grid

### Worked example: Plot a course
Start at X. Each grid square is 10 m. Move 140 m west, 40 m south, 40 m east, 30 m south, 30 m west, 10 m south, 70 m east, 60 m north.

Add up the east-west moves: west $140 + 30 = 170$, east $40 + 70 = 110$. Net: 60 m west.

Add up the north-south moves: south $40 + 30 + 10 = 80$, north $60$. Net: 20 m south.

You finish 60 m west and 20 m south of X.

### Exam tip: Net movement
To find where you finish, total the moves in each direction and cancel opposites: north cancels south, east cancels west.

## Scale and distance

A **scale** tells you how much real distance each unit on the map stands for.

### Worked example: Using a scale
Scale: 1 cm stands for 5 km. Two towns are 7 cm apart on the map. Real distance: $7 \times 5 = 35$ km.

### Worked example: Rings on a map
A city map shows rings around the centre at 5 km, 10 km, 15 km and 20 km. A town on the third ring is about 15 km from the centre. A town halfway between the second and third rings is about 12.5 km from the centre.

### Challenge: Selective level: turning and facing
Ella faces north. She turns $90^\circ$ clockwise, then $135^\circ$ clockwise. Total turn $= 225^\circ$ clockwise. From north: east is $90^\circ$, south is $180^\circ$, south-west is $225^\circ$. She faces **south-west**.

Jack walks 3 km north, 4 km east, 3 km south. He is now 4 km east of where he started, so to get home he walks 4 km west.

**Mind map**

```text
Directions and maps
  Compass
    N E S W clockwise
    NE SE SW NW between
    45° between neighbours
  Describing
    "A is north of B"
    Swap places, flip direction
  Routes
    Total each direction
    North cancels south
  Scale
    Map length x scale
```

## Quick summary

- The compass points in clockwise order are N, NE, E, SE, S, SW, W, NW, each $45^\circ$ apart.
- "A is east of B" means from B you look east to see A. Then B is west of A.
- On a route, total the moves each way. North cancels south, east cancels west.
- Real distance $=$ map distance $\times$ scale.

## Quiz

Try these questions from the chapter quiz.

1. Which direction is opposite to east?
   - A. north
   - B. south
   - C. west
   - D. north-east
   - Answer: C. west. East and west are opposites.

2. Which direction is halfway between north and west?
   - A. north-east
   - B. north-west
   - C. south-west
   - D. south-east
   - Answer: B. north-west. Halfway between north and west is north-west.

3. Sydney is east of Canberra. Canberra is ___ of Sydney.
   - A. east
   - B. west
   - C. north
   - D. south
   - Answer: B. west. Swap the places and the direction flips.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/selective-school-maths/directions-and-maps/#quiz