The distance from a particular point after traveling a distance of X
meters in the horizontal direction and a distance of Y meters in the
vertical direction is equal to X^{2}+y^{2 }(Please note that in common usage, **north-south direction is referred to as "vertical" direction** and **east-west direction is referred to as "horizontal direction**.

To solve these types of problems, the student should know the directions
properly - without any confusion. The following diagram shows all the
directions and the student should memorize the diagram.

If you have problems in remembering the above diagram then just remember
the word NEWS and a reverse S. Of course, this S is not like your
Normal S. Its kinda kiddish. Have a look at the below figure.

Start with N (for North) and move to E, W and finally S. Mark the corner
of North and East as North-East, South and East as South-East and so
on... Well, you have your own diagram now :P

Now lets have discuss this topic with some examples. So that you can
easily understand what exactly is Direction Sense and how to solve the
problems.

**1**. A person travels towards east from his house and travels a
distance of 3 meters; he then travels a distance of 7 meters south wards
and then travels towards east a distance of 3 meters and finally
travels southwards a distance of 10 meters. What is his vertical
distance from his house?

**Solution :**

The distance traveled by him is equal, to** 10 + 7 = 17m. **Have a look at the below figure for detailed understanding.

**2. A person starts from his house and travels 5 meters towards east,
then travels 6 metres towards right, then travels 8 meters towards east
and travels 2 meters towards south after that. Finally he turns right
and travels 7 meters. What is the total distance he has traveled from
his house in the north-south direction? **
**Sol : **The distance he traveled from his house in north-south direction is equal to 6 + 2 = 8 Meters.

**3. A person travels 7 meters towards east, then he turns right and
travels 2 meters; then travels 5 meters towards left and then proceeds 2
meters northwards and finally travels 2 meters westwards. How far is he
from his house in the vertical direction?**
**Sol :** The distance covered by the person in the north-south
direction from his house is equal to 2-2 = 0 meters (Here please keep in
mind that he has actually traveled 2+2 = 4 meters in the north-south
direction but, of that distance, since 2m is towards north and 2m
towards south, effectively, he is 0m away from his house in the
north-south direction).

**4. Starting from one location, a person travels a distance of 5
meters southwards, then travels a distance of 7 meters leftwards, then
travels 5 meters northwards and finally travels 6 meters eastward to
reach a new location. What is the distance he travelled from his
previous location?**
**Sol : **The distance traveled by

** **vertically is 5-5 = 0
meters and the distance travelled horizontally is equal to 7+6 = 13m.
Therefore, the distance travelled from his original location is also
equal to 13m.

**5.
A person starts from his house and goes 2 meters towards east, then
turns towards right and goes 25 meters and again goes towards east
traveling 15 meters and then turns left and travels for 18 meters. He
then goes towards east and travels 7 meters. How far is he from his
house?**
**Sol : **If we represent the path covered by him in a diagram, it will appear as follows.

** **
The total distance travelled horizontally is equal to 2+15+7 = 24
metres and the total distance travelled vertically is 25-18 = 7 metres.

So, the total distance travelled will be equal to root (24

^{2} + 7

^{2 }) = 25m

That's all for now friends. We shall discuss some more practice
exercises on Directions in our next post.All the best and happy reading
:)