Paths on a grid

In your book, Maths Mela (Chapter 14, Maps and Locations), an ant at the zoo goes to collect food. It crawls along the lines of a grid in which each small square is 1 cm long and 1 cm wide. A direction arrow shows north, south, east and west. We describe each path by its distances and directions, starting from where the ant stands.

To get to the laddoos, the ant crawls 2 cm towards the east. To get to the sugar, it crawls 3 cm towards the north. To get to the bread, it crawls 3 cm towards the west, and then 2 cm towards the south. That path is 3 + 2 = 5 cm long.

The path drawn to the apple is longer: 5 cm south, then 3 cm east, then 2 cm north. That is 5 + 3 + 2 = 10 cm. But look where the apple really is. Going 5 cm south and then 2 cm back north leaves the ant just 3 cm south of its start, and it went 3 cm east. So the apple is 3 cm east and 3 cm south of the start.

The book asks for other routes to the apple and which is the shortest. The ant could crawl 3 cm east and then 3 cm south: only 3 + 3 = 6 cm. A route never needs to go back the way it came, so the shortest route uses only the distances it must cover.