Saravana drives 15 km West from his office to the gym. He then turns left and drives 10 km to a supermarket. Next, he turns left and drives 39 km to a petrol pump. Finally, he takes a right turn and drives 22 km to reach his friend's house. In which direction and at what shortest distance is Saravana's office from his friend's house? (All turns are 90^\circ unless specified.)
- A. 40 km, North - west ✓
- B. 2\sqrt{40} km, North - west
- C. 4\sqrt{20} km, South - east
- D. 40 km, North - east
Correct Answer: A. 40 km, North - west
Explanation
Let office be (0,0). Gym = (-15, 0). Supermarket = (-15, -10). Petrol pump = (-15+39, -10) = (24, -10). Friend's house = (24, -10-22) = (24, -32). Distance from house to office = \sqrt{(-24)^2 + 32^2} = 40 km. Direction is North-West.