Uday starts from Point Y and drives 16 km towards the North. He then takes a right turn, drives 28 km, turns right and drives 31 km. He then takes a right turn and drives 13 km. He takes a right turn and drives 41 km. He then turns left, drives 15 km, turns right and drives 8 km to stop at Point Z. How far (shortest distance) and towards which direction should he drive in order to reach Point Y again? (All turns are 90-degree turns only unless specified)
34 km towards South
To solve this problem, we need to track Uday's movements on a coordinate plane, starting from Point Y at the origin (0,0).
- He drives 16 km north, ending at (0,16).
- Turns right (east) and drives 28 km, ending at (28,16).
- Turns right (south) and drives 31 km, ending at (28,-15).
- Turns right (west) and drives 13 km, ending at (15,-15).
- Turns right (north) and drives 41 km, ending at (15,26).
- Turns left (west) and drives 15 km, ending at (0,26).
- Turns right (north) and drives 8 km, ending at (0,34), which is Point Z.
To find the shortest distance back to Point Y (0,0) from Point Z (0,34), we calculate the distance between these two points.
The distance formula in a coordinate plane is: d = √((x2 - x1)² + (y2 - y1)²).
Here, (x1,y1)=(0,34) and (x2,y2)=(0,0). So:
d = √((0-0)² + (34-0)²) = √(0 + 1156) = √1156 = 34 km.
The direction from Point Z to Point Y is south since Y has a lower y-coordinate than Z.
Thus, Uday should drive 34 km towards South to reach Point Y.
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?
