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
Sita took an auto from her home in Andheri (A) to go to her college in Fatehpuri (F). Rather than continuing straight on the direct road to the college that had no turns, the auto driver took a diversion after 10 km and tumed right at Bandra (B) crossing, then at Colaba T- point (C) after 8 km turned left, again after covering 12 km turned left at Dalhousi Building (D) and soon after 8 km turned right at Elphinston point (E) and after covering 4 km reached Fatehpuri (F). Had the auto driver taken the direct route how much less distance would Sita have actually travelled between the starting point and the destination?
Radha walks a distance of 9 m towards the South-East. Then she walks 15 m towards the West. From here, she walks 9 m towards the North-West. Finally she walks 6 m towards the East and stands at the point. How far is she standing from the starting point?
According to the time by Nihaal's watch its half past one and the hour hand is pointing towards the north-east. Assuming that there is no change in Nihaal's position, in which direction would the minute hand point after 30 minutes?
According to the time by Rohan's watch, it is half past 6 and the watch's hands are pointing to the south. In which of the given directions will the minute-hand point AFTER exactly 24 hours?
According to the time by Rick's watch its quarter past eight. If the minute hand points towards the east, towards which direction would the hour hand point?
