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Constructions And Scale Drawings

Constructions And Scale Drawings

Scale drawings and bearings

Scale Drawings Paper 1 + 2 6 min read

On this page
  1. In this note
  2. Formula bank
  3. Scales and maps
  4. Bearings
  5. Ways they test it
  6. Mistakes to avoid
  7. Summary
  8. Practice
  9. Can I do this?
  10. Quiz

In this note

Syllabus 4.3: scale drawings and bearings
  • 4.3Use scale drawings ('1 cm to 2 km') and map ratios (1 : 25 000), including map areas.
  • 4.3Use three-figure bearings measured clockwise from north.
  • 4.3Find a back bearing.

Before you start: Constructing triangles and maps and scales.

Formula bank

ScaleLearn itreal length = drawing length × scaleconvert units at the end (100 000 cm = 1 km).Use it when scale drawings and maps.
Map areasLearn itreal area = map area × (scale)²Use it when an area on a map.
BearingLearn itangle clockwise from north, three figures (065°)Use it when directions.
Back bearingLearn itbearing ± 180°add 180 if under 180°, subtract if over.Use it when 'bearing of A from B'.

Scales and maps

ScaleDrawing → realReal → drawing
1 cm to 2 km× 2 km: 4.6 cm → 9.2 km÷ 2: 15 km → 7.5 cm
1 : 25 000× 25 000 (same units): 6 cm → 150 000 cm = 1.5 km÷ 25 000

General methodHow to use a scale or map ratio

  1. Drawing to real: multiply by the scale. Real to drawing: divide.
  2. With a ratio 1 : n, keep the same units, then convert (cm → m ÷ 100, cm → km ÷ 100 000).
  3. Areas: multiply by n² (a map is a similar shape), then convert (1 km² = 10¹⁰ cm²).

Example A map has scale 1 : 25 000. A lake has area 8 cm² on the map. Find its real area in km².

Square the scale, then convert.

  1. \(8\times25\,000^{2}=5\times10^{9}\) cm²
  2. \(\div10^{10}\)

Answer 0.5 km²

Try it yourself

1
Scale 1 cm to 2 km. AB = 4.6 cm on the drawing. Real distance (km)?
Show answer

Answer 9.2

2
Map 1 : 50 000. Two towns 3.2 km apart. Distance on the map (cm)?
Show answer

Answer 6.4

Bearings

Bearing of B from A is 065°NN065°bearing of A from B: 245°AB
Stand at A, face north, turn clockwise to B: 065°.

A bearing is measured CLOCKWISE from NORTH and written with three figures. 'The bearing of B from A' means stand at A. The back bearing (A from B) differs by 180°: 065° + 180° = 245°.

General methodHow to find or use a bearing

  1. Draw a north line at the point you measure FROM (the word after 'from').
  2. Measure clockwise from north to the line joining the points; write three figures.
  3. Back bearing: add 180° if the bearing is under 180°, otherwise subtract 180°.

Try it yourself

1
The bearing of B from A is 065°. Bearing of A from B?
Show answer

Answer 245

2
The bearing of L from P is 300°. Bearing of P from L?
Show answer

Answer 120

Ways they test it

Type 1 Scale drawing

"The scale is 1 cm to 2 km. Find the actual distance AB." (2 marks)

Spot it a drawing with a scale.

  1. Measure in cm.
  2. × scale.

Type 2 Map area

"Scale 1 : 25 000. Map area 8 cm². Real area in km²?" (3 marks)

Spot it an area on a map.

  1. × scale².
  2. Convert to km².

Type 3 Bearings

"Measure the bearing of B from A" / "find the bearing of A from B". (1-2 marks)

Spot it north lines, two places.

  1. Clockwise from north at the 'from' point.
  2. Back bearing ± 180°.

Type 4 Locate a point

"D is 250 m from C on a bearing of 140°. Mark D." (2 marks)

Spot it a distance and a bearing.

  1. Scale the distance.
  2. Protractor from north at C, clockwise.

Mistakes to avoid

  • ✗ Measuring anticlockwise✓ clockwise from northDefinition.
  • ✗ 65°✓ 065°Three figures.
  • ✗ Map area × 25 000✓ × 25 000²Areas scale by the square.

Summary

  • Real = drawing × scale; drawing = real ÷ scale.
  • Map areas: × (scale)².
  • Bearings: clockwise from north, three figures.
  • Back bearing: ± 180°.

If you see …

  • "bearing of B from A"stand at A.
  • an area on a mapmultiply by the scale squared.

Practice

Practice: easy, medium, hard

Easy

1
Scale 1 cm to 2 km. C is 15 km from A. AC on the drawing (cm)?
Show answer

Answer 7.5

2
Map 1 : 20 000; 4 cm on the map. Real distance (km)?
Show answer

Answer 0.8

3
Bearing of due west?
Show answer

Answer 270

Medium

1
Map 1 : 25 000; 6 cm on the map. Real distance (km)?
Guide me

What is it asking? a distance

What do we know? 6 × 25 000 = 150 000 cm

Plan ÷ 100 000

Show working
  1. 1.5 km

Answer 1.5

2
Bearing of P from Q is 130°. Bearing of Q from P?
Guide me

What is it asking? a bearing

What do we know? under 180°

Plan + 180

Show working
  1. 310°

Answer 310

3
Scale 1 cm to 50 m; 3.4 cm on the drawing. Real length (m)?
Guide me

What is it asking? a length

What do we know? × 50

Plan 3.4 × 50

Show working
  1. 170 m

Answer 170

Hard

1
Map 1 : 25 000; lake area 8 cm² on the map. Real area (km²)?
Guide me

What is it asking? an area

What do we know? × 25 000²

Plan ÷ 10¹⁰

Show working
  1. \(5\times10^{9}\) cm²
  2. 0.5 km²

Answer 0.5

PartAnswer / workingMarksGuidance
\(8\times25\,000^{2}\)M1
\(5\times10^{9}\)A1
0.5A1
Total: 3 marks
2
Map 1 : 40 000. A park has real area 0.8 km². Area on the map (cm²)?
Guide me

What is it asking? an area

What do we know? 0.8 km² = \(8\times10^{9}\) cm²

Plan ÷ 40 000²

Show working
  1. \(8\times10^{9}\div1.6\times10^{9}=5\)

Answer 5

PartAnswer / workingMarksGuidance
\(\div40\,000^{2}\)M1
5A1
Total: 2 marks
3
A field: AC = 400 m, BC = 550 m. Scale 1 cm to 100 m. Compass radius for BC (cm)?
Guide me

What is it asking? a length

What do we know? ÷ 100

Plan 550 ÷ 100

Show working
  1. 5.5 cm

Answer 5.5

PartAnswer / workingMarksGuidance
5.5B1
Total: 1 mark

Can I do this?

Anything unticked: revise that section first. All ticked: take the quiz.

Quiz

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