Q-39. Leela starts from a point and walks 1 km east and then turns left and walks 2 km and again turns right and walks 2 km again. She starts towards a point 2 km towards her right， from where again she walks 1 km left. How far is she from the starting point? (a)3km(b)4 km (c) 5km (d) 2 km a in

To determine how far Leela is from the starting point, let's break down her journey step by step and visualize her movements on a coordinate plane.

1. Starting Point:

   • Let's assume Leela starts at the origin $(0, 0)$.

2. First Movement:

   • She walks 1 km east.
   • New position: $(1, 0)$.

3. Second Movement:

   • She turns left (north) and walks 2 km.
   • New position: $(1, 2)$.

4. Third Movement:

   • She turns right (east) and walks 2 km.
   • New position: $(3, 2)$.

5. Fourth Movement:

   • She starts towards a point 2 km to her right (east).
   • New position: $(5, 2)$.

6. Fifth Movement:

   • She walks 1 km left (west).
   • New position: $(4, 2)$.

Now, we need to find the distance from her final position $(4, 2)$ to the starting point $(0, 0)$.

The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula:

Substituting the coordinates of the starting and final points:

However, the options provided are in whole numbers. Let's approximate $2\sqrt{5}$:

Since the options are whole numbers, we need to re-evaluate the problem to ensure there are no calculation errors. Let's recheck the movements:

1. Starting at $(0, 0)$.
2. Moves to $(1, 0)$.
3. Moves to $(1, 2)$.
4. Moves to $(3, 2)$.
5. Moves to $(5, 2)$.
6. Moves to $(4, 2)$.

The final position is indeed $(4, 2)$, and the distance from $(0, 0)$ to $(4, 2)$ is:

Given the options, the closest whole number is 4 km.

Thus, the correct answer is: $\boxed{4}$