Question:
A man starts from point A and travels 20 km toward North and then 12 km towards west to reach point B. He took a Southward turn and went 5 km to reach point C. Again, he turned Eastward and went 10 km to reach point D. Lastly, he travelled 15 km turning to his right. What is the distance and in which direction is he from his starting point?
A man starts from point A and travels 20 km toward North and then 12 km towards west to reach point B. He took a Southward turn and went 5 km to reach point C. Again, he turned Eastward and went 10 km to reach point D. Lastly, he travelled 15 km turning to his right. What is the distance and in which direction is he from his starting point?
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Use the coordinate system to solve problems involving directions. Assign positive and negative values to the respective directions.
Updated On: Feb 15, 2025
- 15 km, West
- 2 km, South
- 12 km, South
- 2 km, West
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The Correct Option is D
Solution and Explanation
The man follows these steps:
From point A, he moves 20 km North.
Then he turns 12 km West to reach point B.
He then takes a Southward turn and travels 5 km to point C.
After turning Eastward, he travels 10 km to point D.
Lastly, he turns right (South) and travels 15 km.
Now, from point A:
His net North-South movement: \( 20 \, \text{km North} - 5 \, \text{km South} - 15 \, \text{km South} = -2 \, \text{km South} \). His net East-West movement: \( 12 \, \text{km West} - 10 \, \text{km East} = 2 \, \text{km West} \). Thus, he is 2 km West from his starting point.
From point A, he moves 20 km North.
Then he turns 12 km West to reach point B.
He then takes a Southward turn and travels 5 km to point C.
After turning Eastward, he travels 10 km to point D.
Lastly, he turns right (South) and travels 15 km.
Now, from point A:
His net North-South movement: \( 20 \, \text{km North} - 5 \, \text{km South} - 15 \, \text{km South} = -2 \, \text{km South} \). His net East-West movement: \( 12 \, \text{km West} - 10 \, \text{km East} = 2 \, \text{km West} \). Thus, he is 2 km West from his starting point.
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