Amit walked 12 m toward east , then he turned to his right and walked 18 m. He then turned to his right and walked 12 m. He again turned to his right and walked 28 m then the again turned to his right and walked 24 m. At what distance is he from the starting point and in which direction ?

Options

A. 23 m north-east
B. 26 m north - east
C. 26 m west
D. 34 m north-east

Answer

To solve the problem step by step, we can break down Amit's movements and calculate his final position relative to the starting point.

### Step 1: Initial Position
Amit starts at a point, which we will denote as point O (0, 0).

### Step 2: First Movement
Amit walks 12 m toward the east.
- New position after this movement:
- Coordinates: (12, 0)

### Step 3: Second Movement
Amit turns to his right (which is toward the south) and walks 18 m.
- New position after this movement:
- Coordinates: (12, -18)

### Step 4: Third Movement
Amit turns to his right again (now facing west) and walks 12 m.
- New position after this movement:
- Coordinates: (0, -18)

### Step 5: Fourth Movement
Amit turns to his right (now facing north) and walks 28 m.
- New position after this movement:
- Coordinates: (0, 10) [since -18 + 28 = 10]

### Step 6: Fifth Movement
Amit turns to his right one last time (now facing east) and walks 24 m.
- New position after this movement:
- Coordinates: (24, 10)

### Step 7: Calculate Distance from Starting Point
Now we need to calculate the distance from the starting point O (0, 0) to the final position (24, 10). We can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates:
\[ \text{Distance} = \sqrt{(24 - 0)^2 + (10 - 0)^2} = \sqrt{24^2 + 10^2} = \sqrt{576 + 100} = \sqrt{676} = 26 \text{ m} \]

### Step 8: Determine Direction
To find the direction from the starting point to the final position, we note that:
- The final position (24, 10) is to the east (positive x-direction) and north (positive y-direction) from the starting point.
- Therefore, the direction is North-East.

### Final Answer
Amit is 26 m away from the starting point in the North-East direction.

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