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A man starts from a point ‘X’ and walks 3 km Southwards, then he turns left and walks 6 km. In which direction is he from the starting point?
- a)South-West
- b)South-East
- c)West
- d)South
Correct answer is option 'B'. Can you explain this answer?
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Given Information:
- The man starts from point X.
- He walks 3 km Southwards.
- He turns left and walks 6 km.
To Find:
In which direction is he from the starting point?
Solution:
1. Let's assume that the starting point X is the origin of a coordinate system.
2. Since the man walks 3 km Southwards, his position will be 3 km below the starting point X on the y-axis.
3. Now, the man turns left and walks 6 km. Since he is facing West after turning left, his position will be 6 km to the left of his previous position.
4. Therefore, his final position will be 6 km to the left and 3 km below the starting point X.
5. To determine the direction, we can draw a right-angled triangle using the starting point X, the final position, and a vertical line connecting them.
6. The hypotenuse of this triangle represents the shortest distance between the starting point and the final position.
7. Using the Pythagorean theorem, we can calculate the length of the hypotenuse.
- The length of the hypotenuse = sqrt((3 km)^2 + (6 km)^2)
- The length of the hypotenuse = sqrt(9 km^2 + 36 km^2)
- The length of the hypotenuse = sqrt(45 km^2)
- The length of the hypotenuse ≈ 6.71 km
8. Now, let's look at the direction of the final position. It is 6 km to the left and 3 km below the starting point.
- Since it is below the starting point, it is in the South direction.
- Since it is to the left of the starting point, it is in the West direction.
9. Combining these directions, we can conclude that the man is in the South-West direction from the starting point.
10. Therefore, the correct answer is option B) South-East.
- The man starts from point X.
- He walks 3 km Southwards.
- He turns left and walks 6 km.
To Find:
In which direction is he from the starting point?
Solution:
1. Let's assume that the starting point X is the origin of a coordinate system.
2. Since the man walks 3 km Southwards, his position will be 3 km below the starting point X on the y-axis.
3. Now, the man turns left and walks 6 km. Since he is facing West after turning left, his position will be 6 km to the left of his previous position.
4. Therefore, his final position will be 6 km to the left and 3 km below the starting point X.
5. To determine the direction, we can draw a right-angled triangle using the starting point X, the final position, and a vertical line connecting them.
6. The hypotenuse of this triangle represents the shortest distance between the starting point and the final position.
7. Using the Pythagorean theorem, we can calculate the length of the hypotenuse.
- The length of the hypotenuse = sqrt((3 km)^2 + (6 km)^2)
- The length of the hypotenuse = sqrt(9 km^2 + 36 km^2)
- The length of the hypotenuse = sqrt(45 km^2)
- The length of the hypotenuse ≈ 6.71 km
8. Now, let's look at the direction of the final position. It is 6 km to the left and 3 km below the starting point.
- Since it is below the starting point, it is in the South direction.
- Since it is to the left of the starting point, it is in the West direction.
9. Combining these directions, we can conclude that the man is in the South-West direction from the starting point.
10. Therefore, the correct answer is option B) South-East.
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A man starts from a point ‘X’ and walks 3 km Southwards, then he turns left and walks 6 km. In which direction is he from the starting point?a)South-Westb)South-Eastc)Westd)SouthCorrect answer is option 'B'. Can you explain this answer?
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