Akshay starts from Point A and drives 12 km towards the north. He then takes a right turn, drives 15 km, turns right and drives 17 km. He then takes a right turn and drives 18 km. He takes a final right turn, drives 5 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90-degree turns only unless specified.)
3 km to the east
Set up a coordinate grid with Point A at the origin (0, 0). North = +y, East = +x.
Move 1: North 12 km → position (0, 12).
Turn right (now facing East). Move 2: East 15 km → position (15, 12).
Turn right (now facing South). Move 3: South 17 km → position (15, 12 − 17) = (15, −5).
Turn right (now facing West). Move 4: West 18 km → position (15 − 18, −5) = (−3, −5).
Turn right (now facing North). Move 5: North 5 km → position (−3, −5 + 5) = (−3, 0).
Point P is at (−3, 0) and Point A is at (0, 0).
Displacement from P to A: (0 − (−3), 0 − 0) = (3, 0), i.e., 3 km due East.
Hence, Akshay must drive 3 km to the east to reach Point A from Point P.
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Important Questions from Direction and Distance Turns
Starting from her home, a woman walks 10 km towards the west. She turns left and walks 25 km. Again she turns left and walks 10 km. After that, she again turns left and walks 5 km. How far is she from her house now?
A. 35
B. 20
C. 25
D. 40
Lalit walks 9 km east, turns left and walks another 8 km. He again takes a left and walks another 3 km. How far and in which direction is he now from his starting point?
A boy starts from his home northward in order to go to a hotel. He took right turn and took left to reach the hotel. Which direction is the hotel facing?
Arun went 6 m from his home towards south and turned left to cover 8 m. Again he turned left and covered 6 m. He again turned right and covered 4 m. What was the direct distance from his home and which direction was he facing?
Sri walked 4 km towards east from home to school, and he turned three times right side of 6 km respectively. What is the distance between his home and the school?
