Kishan starts from Point A and drives 34 km towards the north. He then takes a right turn, drives 44 km, turns right and drives 46 km. He then takes a right turn and drives 51 km. He takes a final right turn, drives 12 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.)
7 km to the east
Place Point A at the origin with north as +y and east as +x. Driving 34 km north reaches (0, 34), while facing north.
A right turn faces east; 44 km east reaches (44, 34).
A right turn faces south; 46 km south reaches (44, -12).
A right turn faces west; 51 km west reaches (-7, -12).
A final right turn faces north; 12 km north reaches (-7, 0), which is Point P.
Point A (0, 0) lies directly east of Point P (-7, 0) at a distance \(|0 - (-7)| = 7\) km.
Hence, Kishan must drive 7 km to the east to reach Point A again.
Similar Questions
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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?
