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Maps and scale drawings

Maps and scale drawings

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Proportion


Ratio


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Tutor: Labib

Summary

Maps and scale drawings

​​In a nutshell

Reading maps and scale drawings requires using ratio to find out the actual distance in real life compared to the scaled distance on the map.



Scaling

Maps have to be drawn accurately to be useful. However, they are much smaller than what they are trying to map! The way that maps stay accurate despite the size difference is through scaling.


Scaling gives the real life distance in proportion to a length of 1cm1cm​ on the map. The scaling is usually displayed like this:

1cm:5km1cm:5km


This means 11 centimetre on the map corresponds to 55​ kilometres in real life.


Example 1

A map has a scale of 1cm:5km.1cm:5km.

i) Two places on the map are 2.4cm2.4cm apart. How far apart are they in real life?

ii) Two locations are 8km8km apart. How far apart are they on the map?


Part i)

First, write down the scaling:

1cm:5km1cm:5km​​


Multiply both sides by 2.42.4 to find out what length 2.4cm2.4cm corresponds to:

2.4cm=2.4×5km2.4cm=2.4\times5km


2.4cm=12km2.4cm=12km​​


The two places are 12km\underline{12km} apart in real life.


Part ii)

Write down the scaling:

1cm:5km1cm:5km​​


Divide both sides by 55 to find what 1km1km corresponds to on the map:

1km=1÷5cm1km=1\div5cm​​


1km=0.2cm1km=0.2cm​​


Multiply both sides by 88 to find what 8km8km corresponds to on the map:

8km=8×0.2cm8km=8\times0.2cm


8km=1.6cm8km=1.6cm​​


The two locations are 1.6cm\underline{1.6cm} apart on the map.



Compass directions

Compass directions are important when reading maps. It is helpful to memorise the 8 directions.


Maths; Rates of change; KS3 Year 7; Maps and scale drawings

(N)orth

(E)ast

(S)outh

(W)est


(N)orth (E)ast

(S)outh (E)ast

(S)outh (W)est

(N)orth (W)est



Scale drawings

Scale drawings work the same way as maps do - with a scale factor.


Example 2

A scale drawing of a house is drawn on squared paper. One square has side length 2cm2cm. If the scaling is 1cm:0.75m1cm:0.75m, how tall is the actual house (including the flag)?

Maths; Rates of change; KS3 Year 7; Maps and scale drawings


Find how tall the scale drawing is:

The height of the drawing is 66​ squares.


One square is 2cm2cm long.


Hence, the scale drawing is 2cm×6=12cm2cm\times6=12cm in height.


Use the scaling to find out how tall the actual house is:

1cm:0.75m1cm:0.75m​​


12cm=12×0.75m12cm=12\times0.75m​​


12cm=9m12cm=9m​​


The actual house is 9m\underline{9m} tall, including the flag.


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FAQs - Frequently Asked Questions

What is a scale drawing?

What are compass directions?

How do you use maps to find the distance between 2 places?

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