GATE EC 2016 Set 2 — Question 9
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
and start from the same location. travels 10 km East and then 10 km North-East. travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between and at the end of their travel?
Correct answer
(C) 20.61
Solution
Let the starting location be the origin on a Cartesian coordinate system.For person M:
Change in y-coordinate = km.
Final position of M () = .For person N:
Change in y-coordinate = km.
Final position of N () = .Shortest distance between M and N:
Using the distance formula :
km.Rounding to two decimal places, the shortest distance is 20.61 km.The final answer is
1.Travels 10 km East: The position becomes .
2.Travels 10 km North-East: North-East direction is from the East (positive x-axis).
Change in x-coordinate = km.Change in y-coordinate = km.
Final position of M () = .For person N:
1.Travels 5 km South: The position becomes .
2.Travels 4 km South-East: South-East direction is from the East (positive x-axis) or from the South towards East.
Change in x-coordinate = km.Change in y-coordinate = km.
Final position of N () = .Shortest distance between M and N:
Using the distance formula :
km.Rounding to two decimal places, the shortest distance is 20.61 km.The final answer is
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