Given the following directional relationships:

(i) A & B means A is 5m west of B.

(ii) A % B means A is 4m south of B.

(iii) A * B means A is 6m north of B.

(iv) A @ B means A is 4m east of B.

In the expression $F \& G, B \& A \% C \& D \& E * F @ H$, what is the direction of point A with respect to point G?

Question

Given the following directional relationships:

(i) A & B means A is 5m west of B.

(ii) A % B means A is 4m south of B.

(iii) A * B means A is 6m north of B.

(iv) A @ B means A is 4m east of B.

In the expression $F \& G, B \& A \% C \& D \& E * F @ H$, what is the direction of point A with respect to point G?

Accepted Answer

**Solution:**

1. Understand the given symbols:
   - $A \& B$: A is 5m west of B.
   - $A \% B$: A is 4m south of B.
   - $A * B$: A is 6m north of B.
   - $A @ B$: A is 4m east of B.

2. Analyze the expression step-by-step:

Expression: $F \& G, B \& A \% C \& D \& E * F @ H$

- $F \& G$: F is 5m west of G.
   - $B \& A$: B is 5m west of A.
   - $A \% C$: A is 4m south of C.
   - $C \& D$: C is 5m west of D.
   - $D \& E$: D is 5m west of E.
   - $E * F$: E is 6m north of F.
   - $F @ H$: F is 4m east of H.

3. From $B \& A$, since B is west of A, A is east of B.

4. From $A \% C$, A is south of C.

5. From $C \& D$, C is west of D.

6. From $D \& E$, D is west of E.

7. From $E * F$, E is north of F.

8. From $F \& G$, F is west of G.

9. From $F @ H$, F is east of H.

10. To find the direction of A relative to G, consider the chain:

- F is west of G.
    - E is north of F.
    - D is west of E.
    - C is west of D.
    - A is south of C.
    - B is west of A.

11. Plotting roughly:

- Starting at G, move 5m west to F.
    - From F, move 6m north to E.
    - From E, move 5m west to D.
    - From D, move 5m west to C.
    - From C, move 4m south to A.

12. So, relative to G, A is to the northwest:

- West component: from G to F (5m west), plus from F to E (north), then west to D and C.
    - South component from C to A.

Overall, A lies northwest of G.

**Answer:** North-West

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