You might need to pinpoint an even more exact location that lies between the grid lines – The Wicked Queen’s Castle, for instance. In this case, you’ll need to give a six-figure reference to help your friends to find it. The number 216205 tells you the exact location of the castle. The first two numbers tell you to go across the map to line 21 – the fourth and fifth numbers tell you to go up to line 20:
216205.
You then need to imagine each square is divided into 100 smaller squares, each 10 metres wide – ten across and ten up. The third number shows the exact horizontal position: 6. The sixth number shows the exact vertical position: 5.
This tells you that the castle is 60 metres east and 50 metres north of the corner of square 2120.
Clever Co-ordinates
If you know the co-ordinates, or grid references, of two locations, then you can calculate the distance between them. In the map below, an explorer is shown at grid reference 212173 – and he wants to get to Grandma’s House, which is at 252204.
To work out the distance between the two, you can draw a right-angled triangle over the map and use Pythagoras’ theorem. This states that if the squares of the lengths of the two short sides are added, the result is the square of the length of the longest side, or hypotenuse. (See here for more on Pythagoras.) So to find the distance to Grandma’s House – the long side of the triangle – you first have to work out the lengths of the two shorter sides.
Here, the horizontal line shows you how far east Grandma’s House is from the explorer’s current location. The explorer is 20 metres east of grid line 21 and the house is 20 metres east of grid line 25. Each square is equal to 100 metres on the ground, so the horizontal line, A, is 400 metres long.
The vertical line shows you how far north Grandma’s House is from the explorer. He is 30 metres north of line 17 and the house is 40 metres north of grid line 20, so the vertical line, B, is 310 metres long.
Now you can apply Pythagoras’ theorem:
400 × 400 = 160,000 metres, and 310 × 310 = 96,100 metres.
If a2 + b2 = the distance to Grandma’s House squared, and these two figures added together make 256,100, then the house is approximately 500 metres from the explorer (there is a special square-root button on some calculators marked ‘√’ to help you work this out!).
