Discussion
A doctor is located at X and his clinic is located at Y. Since there is no straight road between the two locations, the doctor first goes to A which is about 250 m due South of X, then goes to B which is about 400 m due East of A, then to C which is about 125 m South of B, and finally reaches the clinic at Y which is about 650 m due West of C. With respect to the clinic at Y, the actual direction of the doctor's house at X is :
Answer: B
The doctor's house X is to the North-East of the clinic Y.
Put X at the origin, with east and north positive.
\[ \begin{aligned} A &= (0, -250) \\ B &= (400, -250) \\ C &= (400, -375) \\ Y &= (400 - 650, -375) = (-250, -375) \end{aligned} \]
From Y, X lies 250 m to the east and 375 m to the north, so X is north-east of Y.
The common slip is to give the direction of Y from X, which is south-west, the opposite. Getting only one of the two components right gives north-west or south-east.
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