Tracking Roopa's Movements
We need to find the location of Roopa's office relative to her friend's house. Let's track her path step by step using coordinates, where the office is the origin (0, 0). We'll consider North as the positive y-axis and East as the positive x-axis.
- Start at Office: Roopa starts at (0, 0).
- Move 20 metres North: Her position becomes (0, 0 + 20) = (0, 20).
- Move 50 metres East: Her position becomes (0 + 50, 20) = (50, 20).
- Move 25 metres North: Her position becomes (50, 20 + 25) = (50, 45).
- Move 50 metres West: Her position becomes (50 - 50, 45) = (0, 45). This is the location of her friend's house.
- Move 30 metres East: Roopa moves further to (0 + 30, 45) = (30, 45). This is her final stop after the visit.
Calculating Office Position from Friend's House
The question asks for the distance and direction from Roopa's friend's house to her office.
- Friend's House Coordinates: (0, 45)
- Office Coordinates: (0, 0)
To find the direction and distance from the friend's house to the office, we calculate the displacement vector:
Displacement = (Office Coordinates) - (Friend's House Coordinates)
Displacement = (0, 0) - (0, 45)
Displacement = (0 - 0, 0 - 45)
Displacement = (0, -45)
This vector (0, -45) represents a movement of 0 metres horizontally (East/West) and -45 metres vertically. A negative value on the vertical axis corresponds to the South direction.
Therefore, Roopa's office is 45 metres South of her friend's house.
Similar Questions
- Tina starts from Point Y and drives 4 km towards north. Then, she takes a left turn and drives 2 km, she turns left again and drives 6 km. She then takes a left turn and drives 4 km. Then, she turns right and drives 4 km. She then takes a final right turn and drives 2 km and stops at Point Z. How far (shortest distance) and towards which direction should she drive in order to reach Point Y again? (All turns are 90-degree turns only, unless specified.)
- Xheik starts from Point A and drives 18 km towards East. He then takes a left turn, drives 4 km, turns left and drives 21 km. He then takes a left turn and drives 9 km. He takes a final left turn, drives 3 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90° turns only unless specified.)
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- Read the given paragraph carefully and answer the question.
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- Pallavi walked from her college library, 70 m towards the north, then 60 m towards the east, then 45 m towards the north and then 60 m towards the west. She stopped at this point to buy some candies from a candy shop. She again walked 50 m towards the north. How far and in which direction is Pallavi's college library from the candy shop?
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How far and in which direction is the post office with respect to Jagdish's house?
Important Questions from Direction and Distance
What is the direction of U with respect to P?
What is the shortest distance between R and T?
If a person walks 3m towards the North from point V, takes a right turn and walks for another 15m, which of the following points would he reach?
In which direction is Amit facing at point F?
What is the distance between the starting point and the end point?
