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 90º unless specified.)
40 km, North-west
Take the office as the origin (east and north positive). Driving 15 km west reaches (−15, 0).
A left turn while facing west means facing south: 10 km gives (−15, −10). A left turn from south means facing east: 39 km gives (24, −10).
A right turn from east means facing south: 22 km gives the friend’s house at (24, −32).
From the friend’s house, the office is 24 km to the west and 32 km to the north, so it lies to the north-west.
Shortest distance = \(\sqrt{24^2 + 32^2} = \sqrt{576 + 1024} = \sqrt{1600} = 40\) km.
Hence, the answer is 40 km, North-west.
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What is the direction of U with respect to P?
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