Travel in the RIGHT Direction

The first step for solving the questions using the concept of 'directions': understand the direction chart, which has 8 directions. Have a glance at the figure below.

The first thing you need to remember is that each main direction change undergoes a 900 change in direction e.g. from North to West/East it will be 900 change. But the change between North and North-east is only 450.

The next important point that needs to be kept in mind is that directions problems generally quiz you about the minimum distance, distance by air, crow fly distance etc. For the purpose of solving these questions, we assume all these distances to be along straight lines and between specified points.

Let us go through some practice problems to be able to understand the mechanism adopted for solving these questions.

**Example 1:** A man goes 3 kms. East from point A and then takes a right turn from point B to move 4 kms. to point C. What is the minimum distance between point A and point C?

**Solution:** In order to find the minimum distance between these points, we use a little bit of geometry. We know that the minimum distance between these points will lie along the hypotenuse of the right-angled triangle formed by these points.

Now applying Pythagoras theorem, the distance between the starting point A and final point C is 5 kms i.e. the square root of the sum of squares of 3 and 4.

An important point to learn from this question could be the fact that you might be asked to specify the direction of the specific point, for example, the question might state: "in which direction is he with respect to the starting point". The answer would be Southeast.

Now, in case the question was: "In which direction is the starting point with respect to C"; the answer would be Northwest.

Another question could be: "In which direction is he walking towards point C"; the answer would be South.

While calculating the distance from a starting point to the destination point when the points form a right angled triangle, the prior knowledge of Pythogorian Triplets ( 3-4-5, 5-12-13, 8-15-17 etc.) is generally very helpful in calculating the distances involved as it saves time spent on calculations. Let us solve an example that uses this knowledge.

**Example 2:** A child is looking for his father. He went 90 metres in the East before turning to his right. He went 20 meters before turning to his right again to look for his father at his uncle's place 30 metres from this point. His father was not there. From here he went 100 metres to the North before meeting his father in a street. What is the smallest distance between the starting point and his father's position?

1. 80 metres 2. 100 metres 3. 140 metres 4. 260 metres

**Solution:**

The movement of the child from A to E are as shown in fig.

Clearly , the child meets his father at E.

Now, AF = (AB - FB)

=(AB - DC) = (90 - 30) m = 60 m.

EF = (DE - DF) = (DE - BC)

=(100 - 20) m = 80 m.

Now the distance is square root of (602 + 802 ), which will be 100 metres.

We can clearly see from the above example that knowledge of basic concepts can go a long way in reducing the time you take to solve problems, along with improving your accuracy. Make sure you place sufficient emphasis on the topics such as 'direction based questions', and your performance is surely meant to improve.

*Best Wishes!!
Team Bulls Eye*