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.
Similar Questions
- Mahesh was facing east when he started from home. He took two right turns and one left turn to reach his school. In which direction, is he facing after reaching his school?
Mr. Vasu starts from Point A and drives 23 km towards the south. He then takes a left turn, drives 19 km, turns left and drives 36 km. He then takes a left turn and drives 19 km, turns left drives 9 km. He then takes a right turn and drives 5 km. He takes a final left turn, drives 4 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.)
Anamika starts from Point A and drives 2 km towards the north. She then takes a right turn, drives 5 km, turns right and drives 7 km. She then takes a right turn and drives 8 km. She takes a final right turn, drives 5 km and stops at Point P. How far (shortest distance) and towards which direction should she drive in order to reach Point A again?
(All turns are 90-degree turns only unless specified.)
Mr. Yorly starts from Point A and drives 6 km towards South. He then takes a right turn, drives 37 km, turns right and drives 42 km. He then takes a right turn and drives 47 km. He takes a final right turn, drives 36 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 degrees turns only unless specified.)
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Mr. Yorly starts from Point A and drives 17 km towards East. He then takes a left turn, drives 18 km, turns left and drives 30 km. He then takes a left turn and drives 31 km. He then takes a left turn, drives 9 km, turns left and drives 6 km. He takes a final right turn, drives 4 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 degrees turns only unless specified.)
Mr. Yorly starts from Point A and drives 4 km towards South. He then takes a left turn, drives 23 km, turns left and drives 8 km. He then takes a left turn and drives 41 km. He takes a final left turn, drives 4 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 degrees turns only unless specified.)
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- Rohit walked towards the West and took a turn at $45^\circ$ in the clockwise direction. He again turned at $180^\circ$ in the clockwise direction. Lastly, he turned $270^\circ$ in the anti-clockwise direction. In which direction was Rohit facing at last?
- Ravish Kumar starts running facing towards the south. He runs for 20 m, then takes a left turn, and then runs for another 30 m. Again, he takes a left turn and runs 70 m. He then finally turns left and walks 30 m.
What is the current position of Ravish with respect to the starting point? (All turns are $90^\circ$ turns only)
Important Questions from Direction and Distance Turns
After leaving school, Hemant and Anurag walk towards the north for 1 km to reach a bus stop. From the bus stop, Hemant turns left and walks for 500 m. Then he turns towards his left and walks for 2 km to reach his home. From the bus stop, Anurag turns right and walks for 250 m. Then he turns right and walks for 1 km to reach his home. In which direction is Anurag's home from Hemant's home?
A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house ?
A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point ?
Two friends Xand Ystart running and they run together for 50 m in the same direction and reach a point. Xturns right and runs 60 m, while Yturns left and runs 40 m. Then Xturns left and runs 50 m and stops, while Yturns right and runs 50 m and then stops. How far are the two friends from each other now?
Shekhar starts walking south from his school and then took one right turn, one left turn and one right turn to reach his shop. In which direction is Shekhar with respect to his school?
