Eight persons M through T are standing in such a way that O is 20 m apart from…

Concept

In direction-sense problems, assign coordinates to one reference point and translate each relation into a displacement. East and West change the horizontal coordinate; North and South change the vertical coordinate.

A point is north-west of another when its horizontal displacement is negative and its vertical displacement is positive.

Application

1. Take S as (0, 0). Since R is 15 m north of S, R = (0, 15).

2. R is 40 m west of P, so P is 40 m east of R: P = (40, 15).

3. P is 50 m south of Q, so Q is 50 m north of P: Q = (40, 65).

4. M is 40 m west of Q, giving M = (0, 65).

5. N is 30 m south of M, giving N = (0, 35).

6. O is 20 m west of N, giving O = (-20, 35).

Cross-check

Relative to S = (0, 0), O has displacement (-20, 35): the horizontal component is westward and the vertical component is northward. The independent sign check therefore gives North-West.

Result: O is North-West of S.