Ravi drove 6 km towards East. He then turned right and drove 10 km. He again turned to his right and drove 6 km. He then turned to his left and drove 15 km. At what distance is he from the starting point and in which direction?

Options

A. 25 km, South
B. 21 km, South
C. 15 km, South
D. 21 km, North

Answer

To solve the problem step by step, we will track Ravi's movements and calculate his final position relative to the starting point.

### Step 1: Initial Position
Ravi starts at a point we will call S (starting point).

### Step 2: Move East
Ravi drives 6 km towards the East.
- New position: A
- Coordinates: (6, 0) (assuming S is at (0, 0))

### Step 3: Turn Right and Move South
Ravi then turns right (which is towards the South) and drives 10 km.
- New position: B
- Coordinates: (6, -10)

### Step 4: Turn Right and Move West
Ravi again turns to his right (which is towards the West) and drives 6 km.
- New position: C
- Coordinates: (0, -10)

### Step 5: Turn Left and Move South
Ravi then turns to his left (which is again towards the South) and drives 15 km.
- New position: D
- Coordinates: (0, -25)

### Step 6: Calculate Distance from Starting Point
Now, we need to find the distance from the starting point S (0, 0) to the final position D (0, -25). The distance can be calculated using the formula for distance between two points:
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where:
- \( (x_1, y_1) = (0, 0) \) (starting point S)
- \( (x_2, y_2) = (0, -25) \) (final position D)

Substituting the values:
\[ \text{Distance} = \sqrt{(0 - 0)^2 + (-25 - 0)^2} \]
\[ \text{Distance} = \sqrt{0 + 625} \]
\[ \text{Distance} = \sqrt{625} \]
\[ \text{Distance} = 25 \text{ km} \]

### Step 7: Determine Direction
Ravi's final position D is at (0, -25), which means he is 25 km directly south of the starting point S.

### Final Answer
Ravi is 25 km away from the starting point in the south direction.

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