Distance and Direction | General Test Preparation for CUET UG - CUET Commerce PDF Download

What is Direction?

Direction is the information contained in the relative position of one point with respect to another point without the distance information. Directions may be either relative to some indicated reference or absolute according to some previously agreed upon frame of reference.

Cardinal directions: The four cardinal directions or cardinal points are:

• North
• East
• South
• West

Their initials commonly denote these directions: N, E, S, W.
East and West are at right angles to North and South, with East being in the clockwise direction of rotation from North and West being directly opposite East.

The intermediate directions of the four cardinal directions are:

• North – West
• North – East
• South – West
• South – East

Assumptions:
The direction at the top of the page is always considered as North unless specified in the question.

Finding Out Distance

• The student is generally expected to find out the distance between the starting point and the destination.
• We are expected to find the shortest distance between the two points, i.e., starting point and the destination point.
• To find out this distance, one should draw the diagram showing the actual path followed by the person, along with the distances travelled.
• Finally, the starting point and destination are joined by a straight line, and the distance is measured.
• For this, we use the Pythagoras theorem which is as follows:

Pythagoras Theorem

RULES FOR QUESTIONS REGARDING SHADOWS

• At the time of sunrise, if a man stands facing East, his shadow will be towards West.
• At the time of sunset, the shadow of an object is always in the East.
• If a man stands facing North, at the time of sunrise his shadow will be towards his left and at the time of sunset it will be towards his right.
• At 12:00 noon, the rays of the sun are vertically downward; hence there will be no shadow.

Example: One morning after sunrise, Nandita and Ravi were sitting in a lawn with their backs towards each other. Nandita’s shadow fell exactly towards her left-hand side. Which direction was Ravi facing?

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

Solution: The correct answer is option (d)

Since it was morning and Nandita’s shadow fell exactly to her left-hand side, Nandita was facing North and hence Ravi should be facing South. 

Concepts for Understanding

• The right and left directional movement
• The directional reference point
• The directions of sun rays and shadow
• The correct map versus wrong map
• Directions in clocks
• Directions in seating arrangement

Topic 1: The Right and Left directional movement

The right and left movement of a person is always with reference to the body moving in the scenario. It is not with respect to the person who is solving the questions.

Example: A person is walking towards you, and after walking for a few metres, he takes a right turn. Which direction is he moving?

Sol: The direction we are facing is always assumed as North. Hence, if a person is walking towards us, he is walking facing (towards) South. After taking a right turn, he is moving towards West.

Example: Mr Deepak Mohan walks 5 km towards the South and then turns to the right. After walking 3 km he turns to the left and walks 5 km. What direction is he facing right now?
(a) West
(b) South
(c) North-East
(d) South-West

Ans: (b)
 The right and left movements are with respect to Mr Deepak Mohan. After walking 5 km towards the South, he takes a right turn and now will be facing West. After walking 3 more km he turns left and walks 5 more km. Now he is facing South.
Hence, the answer is option (b).

Topic 2: The directional reference point

Observe the five cities on the map shown below. The five cities are New Delhi, Mumbai, Bengaluru, Chennai, and Kolkata.

The city Bengaluru is exactly below New Delhi, hence Bengaluru is in the South direction with respect to New Delhi, whereas it is in the West direction with respect to Chennai.

Mumbai is in the North-West direction with respect to Bengaluru, whereas Bengaluru is in the South-East direction with respect to Mumbai. One should draw a cardinal direction at a reference city/place to find the direction of the other city.

Example: Mrs Veena wants to go to the Krishna Rajendra market. She moved northwards and after covering some distance turned left and moved 4 km and reached a crossing. The road in front of her led to Jaynagar while the road to her left led to Bangalore Medical College and the road to her right led to the Krishna Rajendra market. In which direction is the Krishna Rajendra market located with reference to the starting point?
(a) West
(b) North-West
(c) South-West
(d) East

Ans: Option (b) is the correct answer.
Mrs. Veena moved north, then left (west) for 4 km.
At the crossing, the Krishna Rajendra Market was to her right (north).
From her starting point, that’s North-West.

Topic 3: The directions of sun rays and shadow

A boy is playing with a skipping rope in the playground and is facing North in the morning. He observes that his shadow was towards his left as the Sun appeared in the East. The boy turned 180 degrees while playing; he is facing South now. His shadow will be towards his right as the Sun is in the East.
  Sunrise/sunset and the shadow  

He does this every day once in the morning and evening. He plays facing South and observes that his shadow was towards his left and then turns and faces North; he observes that his shadow was towards his right. The direction of one’s shadow depends on the direction and time he/she is facing.

The table below summarises the relation of shadow with respect to the direction and time:

Example: One morning after sunrise, Nandita and Ravi were sitting in a lawn with their backs towards each other. Nandita’s shadow fell exactly towards her left-hand side. Which direction was Ravi facing?
(a) East
(b) West
(c) North
(d) South

Ans: (d)
Since it was morning and Nandita’s shadow fell exactly to her left-hand side, Nandita was facing North and hence Ravi should be facing South. Hence the answer is option (d).

Topic 4: Correct Map versus Wrong Map

This section involves the comparison of two maps, one of which is definitely wrong. One has to find the correct direction in the wrong map by applying logical analysis.

Example: At a crossing, there was a direction pole, which was showing all the four correct directions. But due to the wind, it turned such that the West pointer was showing South. Harish went in the wrong direction thinking that he was travelling East. In what direction was he actually travelling?
(a) South
(b) North
(c) West
(d) East

Ans: (b)
The correct answer is option (b), i.e., North.

Topic 5: Directions in Clocks

All the pirates and travellers during the 16th and 17th centuries used the compass as a navigation device, which helped them discover land unknown to mankind. Clocks lacked directional information as their main task was to tell the time.

Adding directions to the clock paved the way for many future inventions. The direction in which the number ‘12’ exists was considered North for reference. The numbers ‘3’, ‘6’, and ‘9’ were considered East, South, and West, respectively.

Example: A clock is placed such that at 2:00 p.m. the minute hand points towards North-West. In which direction does the hour hand point at 6:00 p.m.?
(a) North-West
(b) West
(c) North-East
(d) South-East

Ans: (d)
If the minute hand at 12 indicates North-West, then at 6:00 p.m. the hour hand will point at number 6. Since numbers 12 and 6 are exactly opposite, the opposite of North-West is South-East. Hence, option (d) is correct.

Topic 6: Directions in board games

In this section, directional concepts are applied to popular board games like Chess and Carrom or Snake and Ladder to solve questions.

Example: A chess piece undergoes the following motion during the game. It starts from D-8, reaches H-5, from there reaches A-3, and finally moves to position H-8 where it dies. In what direction was the piece when it died, assuming the chessboard is placed in front of you?

Ans: 

1. Initial Position: Chess piece starts at D-8.
2. Movements:
   • D-8 → H-5 (South-East)
   • H-5 → A-3 (South-West)
   • A-3 → H-8 (North-East)
3. Final Position: H-8
4. Direction at Death: The piece moved North-East to reach H-8.

Correct Answer: North-East 

Example: P, Q, R, and S are playing a game of carrom. P and R, and S and Q are partners. S is to the right of R who is facing West. Then Q is facing?

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

Ans: (a)
Since R is facing West and P is R's partner, P is facing East. Also, S is to the right of R, so S will be facing South and Q is S's partner. Therefore, Q will face North. Hence, option (a) is correct.

Topic 7: Directions of Seating arrangement

This section involves the combination of directional logic with seating arrangement.

Example: J, K, L, M, N, O, P and R are eight huts. L is 2 km east of K. J is 1 km north of K and Q is 2 km south of J. P is 1 km west of Q while M is 3 km east of P and O is 2 km north of P. R is situated exactly in the middle of K and L while N is exactly in the middle of Q and M.
(i) Distance between K and P is
(a) 1.0 km
(b) 1.23 km
(c) 1.41 km
(d) 1.5 km

Ans: (c)
Given Information:L is 2 km east of K.

1. J is 1 km north of K.
2. Q is 2 km south of J. This means:
   • J is 1 km north of K.
   • Q is 2 km south of J, so Q is 1 km south of K.
3. P is 1 km west of Q.

Finding the Distance Between K and P:

• Horizontal distance from K to P = 1 km (since P is west of Q).
• Vertical distance from K to P = 1 km (since Q is 1 km south of K).

Since K, P, and Q form a right-angled triangle, we use the Pythagoras theorem to calculate the shortest distance:

Distance (KP) = √(1² + 1²)
= √(1 + 1)
= √2
= 1.41 km

Correct Answer: Option (c) 1.41 km

(ii) Distance between K and R is:
(a) 1.41 km
(b) 3 km
(c) 2 km
(d) 1 km

Ans: (d)

Given Information:

• L is 2 km east of K.
• R is exactly in the middle of K and L.

Since R is exactly in the middle, the distance from K to R is half of 2 km:

Distance (K to R) = 2 ÷ 2 = 1 km

Correct Answer: Option (d) 1 km

Solved Examples 

Type 1:

Q: Siva, starting from his house, goes 5 km East, then he turns left and goes 4 km. Finally, he turns left and goes 5 km. How far is he from his house and in what direction?

Solution:

From the third position, it is clear he is 4 km from his house and is in the North direction.

Type 2:

Q: Suresh, starting from his house, goes 4 km East, then he turns right and goes 3 km. What minimum distance must he cover to return home?

Solution:

Type 3:

One morning after sunrise, Juhi, while going to school, met Lalli at Boring Road crossing. Lalli's shadow was exactly to the right of Juhi. If they were face to face, which direction was Juhi facing?

Solution: In the morning, the sun rises in the East.

So, in the morning, the shadow falls towards the West.

Now Lalli's shadow falls to the right of Juhi. Hence, Juhi is facing South.

Type 4:

Q: Hema, starting from her house, walked 5 km to reach the crossing of Palace. In which direction was she going? A road opposite to this direction goes to the hospital. The road to the right goes to the station. If the road which goes to the station is just opposite to the road which goes to IT-Park, then in which direction from Hema is the road leading to IT-Park?

Solution:

From the diagram, it is clear that the road leading to IT-Park is to the left of Hema.