Direction: Study the information given below carefully and answer the questions that follow.
What is the shortest distance between point N and point S?
5m
Calculating Shortest Distance Between Points N and S
This problem requires us to determine the straight-line distance between the starting point of the second leg of Dibakar's journey (point N) and his final stopping point (point S). We need to carefully track his movements to find the net displacement.
Tracing Dibakar's Path
Let's break down Dibakar's movements step by step:
- Starts at point M, walks East for 3m to point N.
- From N, turns right (South) and walks 6m to point O.
- From O, turns right (West) and walks 7m to point P.
- From P, turns left (South) and walks 3m to point Q.
- From Q, turns left (East) and walks 11m to point R.
- From R, turns left (North) and walks 6m to point S.
Determining Net Displacement
To find the shortest distance between N and S, we need to calculate the net change in the East-West direction and the North-South direction relative to point N.
Let's analyze the movements relative to point N:
- East-West Movement:
- From N to O: No East-West change.
- From O to P: Moved 7m West.
- From P to Q: No East-West change.
- From Q to R: Moved 11m East.
- From R to S: No East-West change.
- North-South Movement:
- From N to O: Moved 6m South.
- From O to P: No North-South change.
- From P to Q: Moved 3m South.
- From Q to R: No North-South change.
- From R to S: Moved 6m North.
So, point S is 4m East and 3m South of point N.
Calculating Shortest Distance using Pythagorean Theorem
The shortest distance between two points is a straight line. We can visualize the net displacement as the two shorter sides of a right-angled triangle, where the shortest distance is the hypotenuse.
Let the net East displacement be the base ($a = 4$m) and the net South displacement be the height ($b = 3$m).
Using the Pythagorean theorem, the distance ($d$) is calculated as:
$$d^2 = a^2 + b^2$$ $$d^2 = (4 \text{m})^2 + (3 \text{m})^2$$ $$d^2 = 16 \text{ m}^2 + 9 \text{ m}^2$$ $$d^2 = 25 \text{ m}^2$$ $$d = \sqrt{25 \text{ m}^2}$$ $$d = 5 \text{m}$$Therefore, the shortest distance between point N and point S is 5 meters.
Similar Questions
In which direction is point S with respect to point O?
In which direction is point Q with respect to point M?
What is the distance between points B and H?
What is the direction of point E from point A?
Important Questions from Direction and Distance
- Vijendra walks a certain distance, say X metres, from his home towards the west. Then he turns left and walks 23 metres. After that, he turns left and walks 36 metres. Then he turns left again to walk 23 metres. He finally turns left and walks 18 metres to reach his home. Find the value of X.
Gaurav exits from the backdoor of his north-facing house and walks 25 m straight, then he takes a left turn and walks 36 m, then he turns left and walks 47 m. He turns left again and walks 36 m. How far and in which direction is he from his house now?
Reeta is standing facing south-east. First, she turns 135° clockwise. After that, she turns 90 ° anticlockwise. Then she turns 45 ° clockwise, followed by a 135 ° anticlockwise turn. In which direction is she facing now?
Sahasra started running from her house towards the north. After 40 meters she turned left and ran for 75 meters. She then turned right and ran for 30 meters, and again turned right to run 75 meters. In which direction was she running finally?
At the time of sunset, Lopa and Kritika are sitting facing each other. If the shadow of Lopa falls to the right of Kritika, in which direction is Kritika facing?
