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GATE2017 EC-2: GA-4

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Fatima starts from point $P$, goes North for $3$ km, and then East for $4$ km to reach point $Q$. She then turns to face point $P$ and goes $15$ km in that direction. She then goes North for $6$ km. How far is she from point $P$, and in which direction should she go to reach point $P$?

  1. $\text{8 km, East}$
  2. $\text{12 km, North}$
  3. $\text{6k m, East}$
  4. $\text{10 km, North}$
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Migrated from GO Electronics 5 years ago by Arjun

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Fatima traverses like this:-

 

Making right angle triangles, $\unicode{0x25FA} \: PXQ$ & then $ \unicode{0x25FA} \: PZY$. 

So, to reach point $P$ from $Y$ she has to travel =$\sqrt{(10^2-6^2)} = 8 \: km$. (in East direction)

Hence, Correct Answer: $ A. \: 8 \: km, \: East $

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