Simar starts from Point A and drives 10 km towards south. He then takes a right turn, drives 7 km, turns right and drives 12 km. He then takes a right turn and drives 9 km. He takes a final right turn, drives 2 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.)
To determine the distance and direction from Point P back to Point A, we need to trace Simar's movements and find the net displacement.
Tracing Simar's Driving Route
Let's assume the starting Point A is at the origin (0, 0) on a coordinate plane, with North being the positive y-axis and East being the positive x-axis.
- Movement 1: Drives 10 km South. New position: (0, -10).
- Movement 2: Turns right (facing West) and drives 7 km. New position: (-7, -10).
- Movement 3: Turns right (facing North) and drives 12 km. New position: (-7, -10 + 12) = (-7, 2).
- Movement 4: Turns right (facing East) and drives 9 km. New position: (-7 + 9, 2) = (2, 2).
- Movement 5: Turns right (facing South) and drives 2 km. New position: (2, 2 - 2) = (2, 0). This is the final Point P.
Calculating Return Path to Point A
Simar's final position is Point P at (2, 0). The starting Point A is at (0, 0).
- To return to Point A (0, 0) from Point P (2, 0), Simar needs to change his x-coordinate from 2 to 0 and keep his y-coordinate at 0.
- The change in the x-coordinate is $0 - 2 = -2$. A negative change in the x-coordinate represents movement towards the West.
- The change in the y-coordinate is $0 - 0 = 0$. There is no North or South movement required.
- The distance is the magnitude of the change along the x-axis, which is $|-2|$ km = 2 km.
- The direction is West.
Therefore, Simar needs to drive 2 km to the west to reach Point A again.
Important Questions from Direction and Distance
Sita took an auto from her home in Andheri (A) to go to her college in Fatehpuri (F). Rather than continuing straight on the direct road to the college that had no turns, the auto driver took a diversion after 10 km and tumed right at Bandra (B) crossing, then at Colaba T- point (C) after 8 km turned left, again after covering 12 km turned left at Dalhousi Building (D) and soon after 8 km turned right at Elphinston point (E) and after covering 4 km reached Fatehpuri (F). Had the auto driver taken the direct route how much less distance would Sita have actually travelled between the starting point and the destination?
Radha walks a distance of 9 m towards the South-East. Then she walks 15 m towards the West. From here, she walks 9 m towards the North-West. Finally she walks 6 m towards the East and stands at the point. How far is she standing from the starting point?
According to the time by Nihaal's watch its half past one and the hour hand is pointing towards the north-east. Assuming that there is no change in Nihaal's position, in which direction would the minute hand point after 30 minutes?
According to the time by Rohan's watch, it is half past 6 and the watch's hands are pointing to the south. In which of the given directions will the minute-hand point AFTER exactly 24 hours?
According to the time by Rick's watch its quarter past eight. If the minute hand points towards the east, towards which direction would the hour hand point?
