## Direction and Distance

**Introduction:** There are four main directions - East, West, North and South. As per the convention we generally take upward direction of a paper as north direction and remaining directions as shown below:

Other than 4 main direction there are four cardinal directions - North-East (N-E the direction exactly between North and East), North-West (N-W the direction exactly between North and West), South-East (S-E the direction exactly between South and East), and South-West (S-W the direction exactly between South and West) as shown below:

The main formula for Direction questions is Pythagoras Theorem.

As per the Pythagoras theorem a² + b² = c² |

5, 12, 13 and its multiples.

7, 24, 25, and its multiples.

8, 15, 17 and its multiples.

9, 40, 41 and its multiples.

11, 60, 61 and its multiples.

12, 35, 37 and its multiples.

**Example**: Rajesh while doing morning walk, goes 5 km in the East, then he turns to his left and goes 4 km. Finally he turns to his left and goes 5 km. Now how far is he from his house and in what direction?
**Solution**:- The picture below represents each action.

I is: moving 5 km east

II is: after traveling in east direction turning left means in north direction (4 km)

III is: after traveling in north direction turning left means in west direction (5 km)

**Example- **Study the following information and answer the questions given:

Sam walked 5 m towards north from point A and reached point B. He took a right turn from point B and walked 7 m and reached point C. He took a right turn from point and walked 10 m to reach point D. He took another right turn from point D and walked 6 m to reach point E. Sam took a right turn from point E and walked 5 m to reach point F.

1.How far and in which direction is point F from point A?

(a) 1 m towards east

(b) 1 m towards south

(c) 1 m towards north

(d) 1 m towards west

(e) Point A coincides with point F

2. What was the total distance that Sam walked?

(a) 35 m

(b) 38 m

(c) 32 m

(d) 31 m

(e) None of these
**Solution:**

1. (a) 1 m towards east,

2. (e) 5 + 7 + 10 + 6 + 5 = 33 m