**Category : **10th Class

**DIRECTIONS**

There are eight directions.

These are:

East (E), West (W), North (N), South (S), North-East (N-E), North-West (N-W), South-East (S-E and South-West (S-W).

The angle between (East and North) or (North and West) or (South and East) or (South and West) is\[90{}^\circ \].

**Clockwise :** The direction in which the clock moves.

**Anticlockwise :** The opposite direction of the movement of the hands of a clock.

**EXAMPLE**

**Ram starts from his house and goes 15 km northwards, then travels 4 km to the left, the travels 5 km towards the left, then again travels 10 km towards the left, then travels 18 k towards the right, how far and in which direction is he from his house?**

(a) 10 km, South-East (b) 10 km, North-East

(c) 9 km, South-West (d) 9 km, North-West

**Explanation (a): **

Ram's house is at A. His movement is:

\[A\to B\to C\to D\to E\to F\]

The final position of Ram is at F.

Clearly, F is now in South-East from his house at A.

Further, in AAPF, ZAPF = 90°

So, by Pythagoras theorem, we have\[A{{F}^{2}}=\text{ }A{{P}^{2}}+\text{ }P{{F}^{2}}\]

\[\Rightarrow AF=\sqrt{6+64}=\sqrt{100}=10\]km

Thus, Ram is 10 km away from his house and in South-East direction.

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