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Divit starts from point A and drives 4 km towards the East. He then takes two simultaneous right turns and drives 2 km and 4 km, respectively. He takes another right turn and drives 5 km. He then takes a left turn and drives 3 km. He takes a final left turn and drives 3 km to reach point B. How far (shortest distance) and towards which direction should he drive to reach Point A again? (All turns are 90 degrees turns only unless specified.)
3 km north
3 km South
3 km East
3 km West
3 km East
Track the net horizontal and vertical displacements separately using a sign convention (East/North as positive, West/South as negative) and then reverse the result to find the path back to the origin.
Track the net horizontal and vertical displacements separately using a sign convention (East/North as positive, West/South as negative) and then reverse the result to find the path back to the origin.
Coordinate Mapping
Starting at origin (0,0), let East be +x and North be +y. 1. Moves 4 km East: (4,0). 2. Two right turns mean he turns South then West: Moves 2 km South (4,-2), then 4 km West (0,-2). 3. Right turn from West leads North: Moves 5 km North (0, 3). 4. Left turn from North leads West: Moves 3 km West (-3, 3). 5. Left turn from West leads South: Moves 3 km South (-3, 0). Point B is at (-3, 0).
Determining Displacement to A
Point B is at (-3, 0). To return to Point A (0, 0) from Point B (-3, 0), one must move +3 units in the x-direction (East). The shortest distance is 3 km and the direction is East.
A: Incorrect, North is not the direction back to origin. B: Incorrect, South is not the direction back to origin. D: Incorrect, West is the direction away from the origin.
C is correct because the final position of Divit is 3 km West of the starting point A, therefore to return to A, he must travel 3 km towards the East.
In direction puzzles involving multiple turns, always use a grid or coordinate system. It prevents confusion during 'right/left' turn sequences and makes calculating the final displacement a simple addition/subtraction problem.
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