Srinija walked 9 km towards the west from her home, then turned towards the south and walked 11 km. Then, she walked 13 km towards the east, and finally walked 4 km towards the west. How far is Srinija from her initial position?

The correct answer is 11 km.

We solve this by tracking Srinija's position step-by-step on a coordinate grid. Let her starting point (home) be the origin (0, 0), where the positive x-axis points East and the positive y-axis points North.

Step 1: Walked 9 km towards the West
Moving west means the x-coordinate decreases by 9.

New position: (0 - 9, 0) = (-9, 0)

Step 2: Turned South and walked 11 km
Moving south means the y-coordinate decreases by 11.

New position: (-9, 0 - 11) = (-9, -11)

Step 3: Walked 13 km towards the East
Moving east means the x-coordinate increases by 13.

New position: (-9 + 13, -11) = (4, -11)

Step 4: Walked 4 km towards the West
Moving west means the x-coordinate decreases by 4.

New position: (4 - 4, -11) = (0, -11)

Key Observation: After all the east-west movements, Srinija is back at x = 0 — the same east-west column as her home. She is simply 11 km directly south of her starting point.

Step 5: Calculate the straight-line distance from the starting point (0, 0) to final position (0, -11)

Using the distance formula:

d=\sqrt{{(0-0)}^2+{(-11-0)}^2}=\sqrt{0+121}=\sqrt{121}=11

Therefore, Srinija is 11 km away from her initial position.