Learn4MA1Papers 1H, 2H · Higher tierGeometry and trigonometryBearings, scale drawings and symmetry

Geometry and trigonometry · Subtopic 4 of 13

Bearings, Scale Drawings and Symmetry

A bearing is an angle measured clockwise from north, written with three figures. To reverse a bearing, add or subtract $180^\circ$ . Map scales turn real distances into drawn ones, and symmetry describes how a shape fits onto itself.

Cambridge 4024 Paper 1Cambridge 4024 Paper 2Edexcel 4MA1 Papers 1H, 2HEdexcel 4MA1 Papers 1F, 2FAQA 8300 Papers 1–3≈ 25 minRevision 5 · updated 2026-10-27

Section 1 of 14

Learning objectives

Measure and write three-figure bearings, clockwise from north.
Find a back bearing (the bearing of $A$ from $B$ ).
Convert between map distances and real distances using a scale.
Find lines of symmetry and the order of rotational symmetry of a shape.

Pause and think

You walk from home to school on a bearing of $070^\circ$ . Which bearing takes you straight back home?

Section 2 of 14

Core idea

Start hereDirections at sea

At sea there are no roads to follow. Sailors give directions as angles from north: "steer 060" means $60^\circ$ clockwise from north. Combine bearings with distances and trigonometry, and you can plot any course.

The big idea

Bearing: clockwise from north, three figures ( $060^\circ$ ). Back bearing: $\pm180^\circ$ .

1. Bearings

The bearing of B from A is 060°

From A, turn

60^\circ

clockwise from north to face B. The back bearing from B to A is

60^\circ+180^\circ=240^\circ

Worked exampleA ship's course

8 km on $060^\circ$ , then 6 km on $150^\circ$ .

Goal: Distance and bearing from the start.
Strategy: Find the angle at the turn, then Pythagoras and tan.

$\text{back bearing}=240^\circ$
$60+180$ : direction back to the start.
$240-150=90^\circ$
Angle at the turn: right-angled.
$\sqrt{64+36}=10\text{ km}$
Pythagoras.
$\tan^{-1}\tfrac68=36.9^\circ\Rightarrow060+36.9=096.9^\circ$
Angle at the start added to the first bearing.

Answer

10

km on

096.9^\circ

✓ CheckBetween

060^\circ

and

150^\circ

✓.

Common misconceptionTwo-figure bearings Write

060^\circ

, not

60^\circ

2. Symmetry

Symmetry of a regular hexagon: 6 lines, order 6

A regular

n

-sided polygon has

n

lines of symmetry and rotational symmetry of order

n

Line symmetry: fold to match.
Rotational order: how many times it fits in a full turn.

Pause and think

Bearing of A from B is $300^\circ$ . Bearing of B from A?

Summary

Clockwise from north, 3 figures.
Back bearing ±180°.

Bearing: Direction as an angle from north.

HistoryThe compass rose. Medieval sailors used a "compass rose" with

32

named points such as north-north-east. The magnetic compass had reached Europe from China by the 1100s. Three-figure bearings in degrees replaced named points because one number is far harder to mishear over a radio.

Fun factRunways are bearings. The big number painted at the end of an airport runway is its bearing divided by

10

. A runway marked

27

points roughly west (

270^\circ

); the other end of the same strip is marked

09

, the back bearing.

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