Maps are used all the time to help the person reading them understand how areas are laid out. A lot of maps you’ve seen will have been scale drawings – pictures where all the distances between locations on the map are in proportion to distances in real life.

For example, suppose we have a town where the church is 1 mile from the school whilst the supermarket is 2 miles from the school – twice the distance away. Then, if a scale drawing of this town were made, the distance (on this drawing) between the supermarket and the school would still be twice the distance of the church from the school.

Every scale drawing should come with a key – a statement that describes how much the map has been shrunk down to fit on the page, i.e. how much bigger the distances in real-life are than the distances on the page. This is best illustrated with an example.

Example: Below is a scale drawing of a portion of coastline. A boat sets off from point A and travels in a straight line to point B. Work out the distance covered by the boat.

The key, shown in the top right, is telling us that every centimetre on the map represents 2km in real-life. So, we must firstly measure the distance between A and B on the picture.

It’s important to measure as carefully as you can, because measuring with a ruler is not tricky so you will be docked marks if you’re slightly out.

In this case, we see that the distance is 6.7cm. Since the key tells us that each one of the cm is 2km, we get the real-life distance travelled by the boat to be

6.7 \times 2 = 13.4\text{ km}### Example Questions

To find the real-life distance between these points, we need to measure them on the map.

Each one of those centimetres represents 50m, so we get the actual distance between A and B to be

4.9\times 50 = 245\text{ m}

Note: You may have got a different measurement depending on how your device is viewing the image/how it was printed. As long as you multiplied your value correctly by 50 then your answer is still correct.

2) In a city, the bus station is situated 960m away from the train station. A map is drawn using the scale

1cm = 150m

Work out the distance between the bus station and train station on the map.

We need to work out how many cm on the map will represent 960m. Every 1cm amounts to 150m, so we must divide the numbers of metres by 150 to get:

960\div 150=6.4\text{ cm}

We need to work out how many centimetres apart the two places will be on the map. The key tells us each cm represents 3.5km, so we must divide 12.95 by 3.5 to get

12.95\div 3.5=3.7\text{ cm}

Drawing a cross on the line 3.7cm away from New Town, we get an image like the one below:

Note: Your cross may look like it is further away or closer to New Town than the one shown here – this will depend on how your device is viewing the image/how it was printed. As long as you measured 3.7cm in distance from New Town on your image then your answer is correct.

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