Seema went 9 km to west She turned to right and went 7 km. She turned to left and went 8 km. From there she turned back and went 11 km. Then she turned to right are went 7 km. How much distance is she from origin ? (Seema turns every time 90° angle)

Options

A. 9 km
B. 6 km
C. 3 km
D. 7 km

Answer

To solve the problem step by step, let's break down Seema's movements and calculate her final position relative to the origin.

### Step 1: Initial Position
Seema starts at the origin (0, 0).

### Step 2: Move 9 km West
- Moving west means moving in the negative x-direction.
- New position: (0 - 9, 0) = (-9, 0)

### Step 3: Turn Right and Move 7 km
- A right turn from west means she is now facing north.
- Moving north means moving in the positive y-direction.
- New position: (-9, 0 + 7) = (-9, 7)

### Step 4: Turn Left and Move 8 km
- A left turn from north means she is now facing west again.
- Moving west means moving in the negative x-direction.
- New position: (-9 - 8, 7) = (-17, 7)

### Step 5: Turn Back and Move 11 km
- Turning back means she is now facing east.
- Moving east means moving in the positive x-direction.
- New position: (-17 + 11, 7) = (-6, 7)

### Step 6: Turn Right and Move 7 km
- A right turn from east means she is now facing south.
- Moving south means moving in the negative y-direction.
- New position: (-6, 7 - 7) = (-6, 0)

### Step 7: Calculate Distance from Origin
- The distance from the origin (0, 0) to her final position (-6, 0) can be calculated using the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (-6, 0)\).

\[ \text{Distance} = \sqrt{(-6 - 0)^2 + (0 - 0)^2} = \sqrt{(-6)^2} = \sqrt{36} = 6 \text{ km} \]

### Final Answer
Seema is **6 km** away from the origin.

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