The person moves in three different directions: north, east, and southwest. We need to find the displacement of the person from the origin, which is the straight-line distance and direction from the starting point to the final point.

Step 1: Analyzing the Movements
Let's analyze the movements of the person:

1. The person moves 30 m north.
2. Then, the person moves 20 m east.
3. Finally, the person moves 30√2 m in the southwest direction.

Step 2: Finding the Displacement
To find the displacement, we need to add the vector components of each movement. We can represent the movements as vectors:

1. The person moves 30 m north ⟶ Vector A = +30 m north
2. The person moves 20 m east ⟶ Vector B = +20 m east
3. The person moves 30√2 m in the southwest direction ⟶ Vector C = -30√2 m southwest

Step 3: Resolving the Vectors
To add the vectors, we need to resolve them into their x and y components.

1. Vector A = +30 m north ⟶ x-component = 0, y-component = +30 m
2. Vector B = +20 m east ⟶ x-component = +20 m, y-component = 0
3. Vector C = -30√2 m southwest ⟶ x-component = -30 m, y-component = -30 m

Step 4: Adding the Components
Now, we can add the x and y components of the vectors:

x-component = 0 + (+20) + (-30) = -10 m
y-component = +30 + 0 + (-30) = 0 m

The displacement of the person from the origin is (-10 m, 0 m).

Step 5: Interpreting the Displacement
The negative x-component indicates that the person has moved towards the west. Therefore, the displacement is 10 m along the west direction.

So, the correct answer is (c) 10 m along west.

Summary:
The person's displacement from the origin is 10 m along the west direction. The person moves 30 m north, 20 m east, and 30√2 m in the southwest direction. By resolving the vectors and adding their components, we find that the person's final position is 10 m west of the origin.

Zero