Town D is 13 Km. towards the East of town A. A bus starts from town A travels…
2023
Town D is 13 Km. towards the East of town A. A bus starts from town A travels 8 Km. towards West and takes a right turn. After taking the right turn, it travels 5 Km. and reaches town B. From town B the bus takes a right turn again, travels 21 Km. and stops. How far and towards which direction must the travel to reach town D?
- A.
13Km. Towards South
- B.
5Km Towards West
- C.
21Km Towards South
- D.
5Km Towards South
Attempted by 5 students.
Show answer & explanation
Correct answer: D
Solution:
Place Town A at coordinates (0, 0). Let east be the positive x-direction and north be the positive y-direction. Therefore Town D is at (13, 0).
The bus travels 8 km west from A: new position is (0 − 8, 0) = (−8, 0).
It then takes a right turn (facing west, a right turn is north) and goes 5 km north: position becomes (−8, 0 + 5) = (−8, 5). This is Town B.
From Town B it takes another right turn (facing north, a right turn is east) and travels 21 km east: position becomes (−8 + 21, 5) = (13, 5).
Compare this final position (13, 5) with Town D at (13, 0): x-coordinates are the same, y differs by 5 units, so the bus is 5 km north of Town D.
Answer: 5 km towards South.