Discussion
A doctor is located at X and his hospital is located at Y. There is no straight lane from the doctor's house to the hospital. So, the doctor first goes to A which is 600 m due east of X, then goes to B which is 450 m due south of A, then to C which is 120 m due west of B and finally reaches the hospital at Y which is 90 m due north of C. With respect to the hospital the correct direction of the doctors house is
Answer: B
The doctor's house is to the north-west of the hospital.
Take X as the origin, with east and north positive. The doctor goes 600 m east to A (600, 0), 450 m south to B (600, -450), 120 m west to C (480, -450) and 90 m north to Y (480, -360).
So the hospital Y is 480 m east and 360 m south of the house. Seen from the hospital, the house lies 480 m west and 360 m north, that is, north-west. South-east is the direction of the hospital from the house, the reverse of what is asked.
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