Town D lies 13 km East of town A. A bus starts at A, goes 8 km West, turns right and goes 5 km to reach B, then turns right again and travels 21 km to stop. How far and in which direction must it travel now to reach town D?
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A13 Km. towards South
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B5 Km. towards West
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C21 Km. towards South
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D5 Km. towards South
Answer
Correct Answer: 5 Km. towards South
Explanation
Introduction / Context:This path-tracking problem mixes absolute placements (D relative to A) with the bus’s movement segments. Converting the description into coordinates clarifies the final short leg required to reach D.
Given Data / Assumptions:
- D is 13 km East of A.
- Segment 1: from A, 8 km West.
- Right turn from West → North; go 5 km to B.
- Right turn from North → East; go 21 km; stop.
Concept / Approach:Use a coordinate frame with A at (0,0). Track each move and compare the final stop with D’s coordinate. The last required move is simply the vertical difference between the stop and D.
Step-by-Step Solution:
Let A = (0,0); D = (13,0).After 8 km West: (−8,0).Right to North, +5 km: (−8,5).Right to East, +21 km: (13,5).To reach D (13,0): move 5 km South.Verification / Alternative check:Plot the points: the final x matches D exactly (13); only y differs by +5.
Why Other Options Are Wrong:
- 13 km South/21 km South: exaggerate the needed vertical correction.
- 5 km West: would change x, which already matches D.
Common Pitfalls:Forgetting that a right turn from North leads to East; swapping axes signs.
Final Answer:5 Km. towards South