According to geography, there are 8-directions:

• 4-cardinal directions – North, South, East, and West
• 4-subsidiary directions – North-East, North-west, South-east, South-west

DIRECTION OF RIGHT TURN: Clockwise

DIRECTION OF LEFT TURN: Anti-clockwise

PYTHAGORAS THEOREM:

This theorem is sometimes needed to find out the distance covered by an individual in the question.

It states that in a right-angled triangle the length of the hypotenuse is equal to the square root of the sum of squares of the other two sides.

Where H=Hypotenuse

             X=Height

             Y=Base

Therefore, according to the theorem H² = X² + Y²

i.e., H= √(X²+ Y²)

IMPORTANT POINTS TO REMEMBER WHILE SOLVING DISTANCE-DIRECTION QUESTION:

–        To know the directions on the plane of paper

–        To sketch out the directions as per the instructions in the question

–        To remember that on the surface of paper

• The direction of right turnis always in the clockwise direction
• The direction of left turnis always in the anti-clockwise direction
• The direction of Northis upwards
• The direction of Southis downwards
• The direction of Eastis ‘to the right’
• The direction of West is ‘to the left’

–        To formulate a step by step analysis of directions and distances

–        To find the final direction or the distance between the starting and final point or both

QUESTION:

Ajith walks 10km towards North. From there he walks 6km towards south, then he turns left and walks 3km.

1)    At what distance is Ajith from the original position?

(a)  7km          (b) 5km          (c) 3km          (d) 4km

2)    In which direction is Ajith with reference to his starting point?

(a)  North-East          (b) West          (c) South-East          (d) East

SOLUTION:

• Take the starting point as ‘A’
• Now, Ajith walks 10km towards North.
• The point 10km to the north is taken as ‘B’, AB=10km
• ‘From there he walks 6km towards south’i.e., from B Ajith walks 6km downwards again.
• The point at 6km towards south is taken as ‘C’, such that BC=6km
• So AC=4km[AB-BC=10-6=4]
• ‘then he turns left and walks 3km’i.e., he turns in the anti-clockwise direction from ‘C’ i.e., towards east and walks 3km in the same direction
• The point 3km in the east is taken as ‘D’, such that CD=3kmand D is the end point of the journey of Ajith

1)    At what distance is Ajith from the original position?

(a)7km          (b) 5km          (c) 3km          (d) 4km

• Starting point of Ajith is ‘A’
• End point of Ajith is ‘D’
• Therefore, the distance of Ajith from the original position is the distance between A and D
• To find AD, Consider right angle triangle, ACD

AD = hypotenuse = X

AC = 4km

CD = 3km

By Pythagoras theorem, X² = AC² + CD² = 4² + 3² = 16+9

                                          X² = 25

                                     X = √25 = 5km

• Therefore, distance at which Ajith is from the original position is 5km

ANSWER: (b) 5km

If the question was:

What is the total distance covered by Ajith?

Then the answer will be the sum of all the distances given in the question irrespective of their directions.

i.e., 10km+6km+3km = 19km

 2)    In which direction is Ajith with reference to his starting point?

(a)  North-East          (b) West          (c) South-East          (d) East

• Present positionof Ajith is at ‘D’
• Now, the direction in which Ajith is with respect to his starting point (A) is asked
• The answer is the direction in which point ‘D’is present with respect to point ‘A’, which clearly is towards the North-East direction as per the final figure.

ANSWER: (a) North-East

If the question was:

          In which direction is Ajith facing?

• Then the answer would have been (d) East.
• Direction faced by point D