Kanika drives 6 km west from her home and turns left and drives 3 km and then turns left again and drives 10 km to reach her office. What is the shortest distance between her home and office?

5

The correct answer is Option (2) → 5

Step 1: Represent the moves

1. Kanika starts at home: (0, 0)
2. Drives 6 km west:
   New position: (-6, 0)
3. Turns left (from west, left → south) and drives 3 km:
   New position: (-6, -3)
4. Turns left again (from south, left → east) and drives 10 km:
   New position: $(-6 + 10, -3) = (4,-3)$ → office

Step 2: Shortest distance (straight line) from home (0, 0) to office (4, -3)

Use distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$d = \sqrt{(4-0)^2 + (-3-0)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ km}$