Question

You are standing in a class – room facing north. In what direction you are facing after making a quarter turn?

Answer 1

Hint: First of all draw the directions “North, South, East and West”. Then show the facing in a class – room in the north direction by an arrow. Now, it is given that if we make a quarter turn from this position which direction we are facing. There are two ways in which we can make a turn either clockwise or anticlockwise. If we start from one direction and come again to the same direction then we have completed an angle of ${{360}^{\circ }}$ so one quarter turn is one – fourth of ${{360}^{\circ }}$ meaning ${{90}^{\circ }}$. Then according to direction placement we can find in clockwise turning in which direction we are facing and similarly with the anti clockwise turning.

Complete step-by-step answer:
In the below diagram, we have shown the directions North, South, East and West by N, S, E and W respectively in the following way:

Now, it is given that in the class – room, we are facing towards north direction so we are showing facing towards north direction by a pink colored arrow as follows:

The quarter turn from any position in this direction placement is equal to one – fourth of ${{360}^{\circ }}$. As you can see from the above figure, that if we start from east direction and then when again come to east direction then we have traversed an angle of ${{360}^{\circ }}$ so if we want to traverse quarter of the full turn we have to traverse one – fourth of ${{360}^{\circ }}$. And one – fourth of ${{360}^{\circ }}$ is equal to:
$\begin{align}
  & \dfrac{1}{4}\left( {{360}^{\circ }} \right) \\
 & ={{90}^{\circ }} \\
\end{align}$
Now, there are two ways in which we can make a quarter turn from north either we can turn anti clockwise or clockwise from this position.
If we make a quarter turn in an anti clockwise sense then we are facing towards the west which we have shown in the below figure by the pink arrow.

If we make a quarter turn in clockwise sense then we are facing towards the east which we show in the below figure by a pink arrow.

Hence, we have shown that if we quarter turn anti clockwise from north then we are facing towards west direction and when we quarter turn clockwise direction then we are facing towards east direction.

Note: The mistake that is likely to happen in this problem is that you might forget to consider both the sense of turns (clockwise and anti clockwise). There are two possibilities here, either you only consider clockwise or only consider anti clockwise sense. But both are possible because it is not specifically given in the question that you have to consider clockwise turn or anti clockwise turn.
And there is a trick to remember this directions cross that we have drawn above and which we are showing again in the below diagram.

The trick is using the initials of the 4 directions i.e. NEWS you can remember the arrangement of these directions.