House Positions Explained

The question asks us to find the direction of house A relative to house C. We are given the relative locations of four houses: B, C, D, and A.

• B is 40 m north of C.
• A is 20 m east of D.
• C is 30 m west of D.

To solve this, we need to combine these pieces of information to determine the exact location of A with respect to C.

Solving the Relative Direction Puzzle

Let's analyze the location data step-by-step:

1. C relative to D: The statement "C is 30 m west of D" means that D is located 30 m towards the East from C.
2. A relative to D: The statement "A is 20 m east of D" means that A is located 20 m further towards the East starting from D.
3. Combining Directions from C: To find A's position relative to C, we combine the eastward movements.

   First, move from C to D, which is $30 \text{ m}$ to the East.

   Then, move from D to A, which is another $20 \text{ m}$ to the East.

   The total eastward displacement from C to A is the sum of these two distances:

   Total Eastward Distance$_{C \to A}$ = Distance$_{C \to D}$ (East) + Distance$_{D \to A}$ (East)

   Total Eastward Distance$_{C \to A}$ = $30 \text{ m} + 20 \text{ m} = 50 \text{ m}$

4. North-South Position: The information about house B ("B is 40 m north of C") describes B's location relative to C but does not provide any North-South information linking A to C or D. Since A is described only as being East of D, and C is West of D, we assume A, D, and C lie on the same East-West line in this context. Therefore, A is directly East of C.
5. Final Direction Determination: Based on the combined eastward movements, house A is located 50 meters directly East of house C.

Final Directional Answer

Consequently, with reference to C, house A is situated in the East direction.