Neha starts from her home and walks 25 km south. She then turns left and walks 20 km. After that, she turns left again and walks 10 km. Finally, she turns right and walks 8 km to reach her school. How far (shortest distance) and in which direction is the school from Neha's home? (All turns are 90º unless specified.)
√1009 km, south-east
Take the home as the origin, east as the positive x-direction and north as the positive y-direction. A left turn while facing south points east, a left turn while facing east points north, and a right turn while facing north points east.
Step 1 — 25 km south: position (0, −25).
Step 2 — Turn left (now facing east), 20 km: position (20, −25).
Step 3 — Turn left (now facing north), 10 km: position (20, −15).
Step 4 — Turn right (now facing east), 8 km: school at (28, −15).
Step 5 — Distance = \(\sqrt{28^2 + 15^2} = \sqrt{784 + 225} = \sqrt{1009}\) km. The school is east and south of the home, i.e. south-east.
20 km and 22 km are smaller than \(\sqrt{1009} \approx 31.8\) km, south-west would need the school to lie west of the home, and north-west is the opposite side altogether.
√1009 km, south-east option is correct.
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