# In which direction is point E with respect to the point D and what is the shortest distance between point F and point D?

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Starting from his home, Kay moves 40km towards North. He then takes a right turn and walks 30 km to reach point D. From there, he turns towards North-West and moves 50 km. After which he moved 40 km towards North and reaches a point which is in line with his home and the point where he took the first turn. Then, he turns and travels towards South-West for 80√2 km to reach point F which is inline with point D and the point where he took the first turn. From F, he finally turned 135 degrees towards his right and walked 80 km to reach point E.

Q: In which direction is point E with respect to the point D and what is the shortest distance between point F and point D?

posted May 1, 2018

See schematic picture for details:
1. E is on the west from D
2. Distance FD = ?
Distance FD is equal to the length of horizontal blue line + 30 km
To find it we need to find the length of vertical blue line, which is = 40 km as side of triangle with hypotenuse of 50 km and other side of 30 km.
Horizontal blue line = sqrt(2*80^2-(40+40)^2)=sqrt(80^2)=80 km, hence FD=80+30=110 km

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