Directions

Theory

In this type of questions, we are asked about the direction of an individual relative to the initial direction. We all know about the major four directions: North, South, East and West. There are 4 intermediary directions: North- East, North-West, South-East and South-West. These 4 intermediary directions are 45 degrees to the North and South directions as shown :

Tip

If you turn in the same way (left/right) 4 times, then you end up going in the same direction as you were before you started turning.

Tip

To solve these questions, visualize yourself standing and facing a given direction.
• If you are facing North then, East is to your right and West to your left
• If you are facing South then, West is to your right and East to your left
• If you are facing East then, South is to your right and North to your left
• If you are facing West then, North is to your right and South to your left

Solved Example

Stephen cycled 20 km south, followed by 30 km east, and followed by 60 km north. How many km should he cycle back to reach his starting point?
Explanation:
Stephen is 30 km east and 40 km north from the starting point. So, he should cycle $$\sqrt{40^2 + 30^2}$$ = 50 km to reach his starting point.

Solved Example

Suraj walks 15 metres towards North-West and then turns right. Then he walks another 10 metres and takes a left turn. He then walks 5 metres. Which direction is he facing finally?
Explanation:
He turned right from North-West. So, he was then facing North-East. He then takes a left turn. So, he is back to North-West.