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?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5
Step 1: Represent the moves
- Kanika starts at home: (0, 0)
- Drives 6 km west:
New position: (-6, 0) - Turns left (from west, left → south) and drives 3 km:
New position: (-6, -3) - 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:
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
$d = \sqrt{(4-0)^2 + (-3-0)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ km}$