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A person starts from a point A and travels 3 km
eastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. The shortest distance between the starting point and the Destination is?
eastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. The shortest distance between the starting point and the Destination is?
Most Upvoted Answer
A person starts from a point A and travels 3 kmeastwards to B and then...
Understanding the Journey from A to D
The journey involves several segments that can be visualized on a coordinate system. Let’s break down the movements step by step.
Step 1: Movement from A to B
- Starting Point A (0, 0).
- Travels **3 km east** to point B (3, 0).
Step 2: Movement from B to C
- At point B, the person turns **left (north)** and travels **3 times the distance** from A to B.
- This distance is **3 km × 3 = 9 km** north.
- Therefore, point C is at (3, 9).
Step 3: Movement from C to D
- At point C, the person turns **left (west)** and travels **5 times the distance** from A to B.
- This distance is **3 km × 5 = 15 km** west.
- Thus, point D is at (3 - 15, 9) = (-12, 9).
Calculating the Shortest Distance from A to D
- The coordinates of point A are (0, 0) and point D are (-12, 9).
- The shortest distance can be calculated using the distance formula:
\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
- Plugging in the values:
\[
\text{Distance} = \sqrt{((-12 - 0)^2 + (9 - 0)^2)} = \sqrt{144 + 81} = \sqrt{225} = 15 \text{ km}
\]
Conclusion
The shortest distance between the starting point A and the destination D is **15 km**. This analysis illustrates the importance of visualizing movements in a coordinate plane for clarity in problem-solving.
The journey involves several segments that can be visualized on a coordinate system. Let’s break down the movements step by step.
Step 1: Movement from A to B
- Starting Point A (0, 0).
- Travels **3 km east** to point B (3, 0).
Step 2: Movement from B to C
- At point B, the person turns **left (north)** and travels **3 times the distance** from A to B.
- This distance is **3 km × 3 = 9 km** north.
- Therefore, point C is at (3, 9).
Step 3: Movement from C to D
- At point C, the person turns **left (west)** and travels **5 times the distance** from A to B.
- This distance is **3 km × 5 = 15 km** west.
- Thus, point D is at (3 - 15, 9) = (-12, 9).
Calculating the Shortest Distance from A to D
- The coordinates of point A are (0, 0) and point D are (-12, 9).
- The shortest distance can be calculated using the distance formula:
\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
- Plugging in the values:
\[
\text{Distance} = \sqrt{((-12 - 0)^2 + (9 - 0)^2)} = \sqrt{144 + 81} = \sqrt{225} = 15 \text{ km}
\]
Conclusion
The shortest distance between the starting point A and the destination D is **15 km**. This analysis illustrates the importance of visualizing movements in a coordinate plane for clarity in problem-solving.
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A person starts from a point A and travels 3 kmeastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. The shortest distance between the starting point and the Destination is?
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A person starts from a point A and travels 3 kmeastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. The shortest distance between the starting point and the Destination is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A person starts from a point A and travels 3 kmeastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. The shortest distance between the starting point and the Destination is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person starts from a point A and travels 3 kmeastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. The shortest distance between the starting point and the Destination is?.
A person starts from a point A and travels 3 kmeastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. The shortest distance between the starting point and the Destination is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A person starts from a point A and travels 3 kmeastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. The shortest distance between the starting point and the Destination is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person starts from a point A and travels 3 kmeastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. The shortest distance between the starting point and the Destination is?.
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