# 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 $1cm$ on the map. The scaling is usually displayed like this:

$1cm:5km$

This means $1$ centimetre on the map corresponds to $5$ kilometres in real life.

##### Example 1

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

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

*ii) Two locations are $8km$ apart. How far apart are they on the map?*

*Part i)*

*First, write down the scaling:*

*$1cm:5km$*

*Multiply both sides by $2.4$ to find out what length $2.4cm$ corresponds to:*

$2.4cm=2.4\times5km$

$2.4cm=12km$

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

*Part ii)*

*Write down the scaling:*

*$1cm:5km$*

*Divide both sides by $5$ to find what $1km$ corresponds to on the map:*

*$1km=1\div5cm$*

*$1km=0.2cm$*

*Multiply both sides by $8$ to find what $8km$* *corresponds to on the map:*

$8km=8\times0.2cm$

$8km=1.6cm$

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

## Compass directions

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

| (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 $2cm$. If the scaling is $1cm:0.75m$, how tall is the actual house (including the flag)?*

*Find how tall the scale drawing is:*

*The height of the drawing is $6$ squares.*

*One square is *$2cm$* long.*

*Hence, the scale drawing is $2cm\times6=12cm$ in height.*

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

$1cm:0.75m$

$12cm=12\times0.75m$

$12cm=9m$

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