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After walking 6kms, I turned right and c...

After walking 6kms, I turned right and covered a distance of 2 kms, then turned left and covered a distance of 10 kms. In the end, I was moving towards the North. From which direction did I start my journey ?

A

North

B

South

C

East

D

West

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we need to analyze the movements described in the question and determine the starting direction based on the final direction being North. ### Step-by-Step Solution: 1. **Starting Point**: Let's assume we start at a point and denote it as the origin (0,0). 2. **First Movement**: The first instruction is to walk 6 km. Since we don't know the starting direction yet, we will analyze each option later. For now, let's denote this movement as moving in a straight line from the starting point. 3. **Turning Right**: After walking 6 km, we turn right. The direction we face after turning right depends on the initial direction: - If we started North, turning right means we face East. - If we started South, turning right means we face West. - If we started East, turning right means we face South. - If we started West, turning right means we face North. 4. **Second Movement**: We then cover a distance of 2 km in the direction we are now facing (after the right turn). 5. **Turning Left**: After covering 2 km, we turn left. Again, the direction we face after turning left depends on our current direction: - If we were facing East, turning left means we face North. - If we were facing West, turning left means we face South. - If we were facing South, turning left means we face East. - If we were facing North, turning left means we face West. 6. **Third Movement**: We then cover a distance of 10 km in the new direction we are facing after the left turn. 7. **Final Direction**: The problem states that after all these movements, we end up facing North. We need to analyze each starting direction option to see which one allows us to end up facing North. ### Analyzing Each Option: - **Option 1: Starting from North**: - Move 6 km North → (0, 6) - Turn right (now facing East) → Move 2 km East → (2, 6) - Turn left (now facing North) → Move 10 km North → (2, 16) - Final direction: North (Correct) - **Option 2: Starting from South**: - Move 6 km South → (0, -6) - Turn right (now facing West) → Move 2 km West → (-2, -6) - Turn left (now facing South) → Move 10 km South → (-2, -16) - Final direction: South (Incorrect) - **Option 3: Starting from East**: - Move 6 km East → (6, 0) - Turn right (now facing South) → Move 2 km South → (6, -2) - Turn left (now facing East) → Move 10 km East → (16, -2) - Final direction: East (Incorrect) - **Option 4: Starting from West**: - Move 6 km West → (-6, 0) - Turn right (now facing North) → Move 2 km North → (-6, 2) - Turn left (now facing West) → Move 10 km West → (-16, 2) - Final direction: West (Incorrect) ### Conclusion: The only option that results in facing North at the end of the journey is starting from the North. **Final Answer**: The journey started from the North.

To solve the problem step by step, we need to analyze the movements described in the question and determine the starting direction based on the final direction being North. ### Step-by-Step Solution: 1. **Starting Point**: Let's assume we start at a point and denote it as the origin (0,0). 2. **First Movement**: The first instruction is to walk 6 km. Since we don't know the starting direction yet, we will analyze each option later. For now, let's denote this movement as moving in a straight line from the starting point. ...
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