A person starts to walk from a ground in the west direction to reach his home. After 13km he reaches at point Y. From point Y, he takes a right turn, walks 7 km and reaches point C. From point C, he takes a left turn, walks 9km and reaches point T. From point T, he takes a left turn and walks 4km and reaches his home. What is the shortest distance between his home and point Y?
\(3\sqrt{10}\) km
Take Y as the origin (0, 0).
Walking west, a right turn faces north: Y → C is 7 km north, so C = (0, 7).
Facing north, a left turn faces west: C → T is 9 km west, so T = (−9, 7).
Facing west, a left turn faces south: T → home is 4 km south, so home = (−9, 3).
Distance from Y = \(\sqrt{9^2+3^2}=\sqrt{81+9}=\sqrt{90}=3\sqrt{10}\) km.
Hence, the shortest distance between his home and point Y is \(3\sqrt{10}\) km.
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?
Rohan walks 10 km towards north from a point A. Then he turns right and walks 6 km. Then, he again turns right and walks 10 km. In which direction is he now from the starting point?
