Shilpa walks 6 km towards South. From there, she walks 9 km towards East. Then…

To find the straight-line (bee-line) distance after several movements along the North-South and East-West directions, first combine all movements along each axis separately to get one net North-South displacement and one net East-West displacement. Since these two net displacements are always perpendicular to each other, the straight-line distance from the starting point is the hypotenuse of a right triangle, given by the Pythagorean theorem: distance = √(net vertical displacement² + net horizontal displacement²).

1. Combine the two southward movements: 6 km + 2 km = 8 km net displacement towards South.

2. Combine the eastward and westward movements: 9 km East − 3 km West = 6 km net displacement towards East.

3. These two net displacements, 8 km South and 6 km East, are perpendicular to each other and form the two legs of a right triangle whose hypotenuse is the distance from the starting point.

4. Apply the Pythagorean theorem: distance = √(82 + 62) = √(64 + 36) = √100 = 10 km.

Cross-check: 8, 6, 10 form the well-known 6-8-10 right triangle (a scaled-up 3-4-5 Pythagorean triple), confirming the result independently.

So, Shilpa is 10 km away from her original position.