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Ravi left home and cycled 10 km towards South, then turned right and cycled 5 km and then again turned right and cycled 10 km. After this he turned left and cycled 10 km. How many kilometers will he have to cycle to reach his home straight?
- a)10 km
- b)15 km
- c)20 km
- d)25 km
Correct answer is option 'B'. Can you explain this answer?
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Ravi left home and cycled 10 km towards South, then turned right and c...
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Understanding Ravi's Journey
Ravi's cycling journey can be visualized as a series of movements on a coordinate plane. Let's break down his movements step by step.
Step-by-Step Movements
- Starting Point: Ravi begins at his home (0, 0).
- First Movement: He cycles 10 km South.
- New Position: (0, -10)
- Second Movement: He turns right (now facing West) and cycles 5 km.
- New Position: (-5, -10)
- Third Movement: He turns right again (now facing North) and cycles 10 km.
- New Position: (-5, 0)
- Fourth Movement: He turns left (now facing West) and cycles 10 km.
- New Position: (-15, 0)
Calculating Distance to Home
To find out how far Ravi is from his starting point (0, 0), we calculate the straight-line distance from his final position (-15, 0) back to (0, 0).
Distance Formula
- The formula for distance between two points (x1, y1) and (x2, y2) is:
Distance = √((x2 - x1)² + (y2 - y1)²)
- Applying Ravi's coordinates:
Distance = √((0 - (-15))² + (0 - 0)²)
Distance = √(15² + 0²)
Distance = √225
Distance = 15 km
Conclusion
Ravi is 15 km away from his home. Therefore, the correct answer is option 'B' – he will have to cycle 15 km to reach his home straight.
Ravi's cycling journey can be visualized as a series of movements on a coordinate plane. Let's break down his movements step by step.
Step-by-Step Movements
- Starting Point: Ravi begins at his home (0, 0).
- First Movement: He cycles 10 km South.
- New Position: (0, -10)
- Second Movement: He turns right (now facing West) and cycles 5 km.
- New Position: (-5, -10)
- Third Movement: He turns right again (now facing North) and cycles 10 km.
- New Position: (-5, 0)
- Fourth Movement: He turns left (now facing West) and cycles 10 km.
- New Position: (-15, 0)
Calculating Distance to Home
To find out how far Ravi is from his starting point (0, 0), we calculate the straight-line distance from his final position (-15, 0) back to (0, 0).
Distance Formula
- The formula for distance between two points (x1, y1) and (x2, y2) is:
Distance = √((x2 - x1)² + (y2 - y1)²)
- Applying Ravi's coordinates:
Distance = √((0 - (-15))² + (0 - 0)²)
Distance = √(15² + 0²)
Distance = √225
Distance = 15 km
Conclusion
Ravi is 15 km away from his home. Therefore, the correct answer is option 'B' – he will have to cycle 15 km to reach his home straight.
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Ravi left home and cycled 10 km towards South, then turned right and cycled 5 km and then again turned right and cycled 10 km. After this he turned left and cycled 10 km. How many kilometers will he have to cycle to reach his home straight?a)10 kmb)15 kmc)20 kmd)25 kmCorrect answer is option 'B'. Can you explain this answer?
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