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A person travels in the following directions: First moves 6 km West, then 6 km South, then 4 km west, and finally 8 km West. What is the net displacement of the person from the starting point?
18 km West, 6 km South
12 km West, 6 km South
14 km West, 8 km South
20 km West, 4 km South
20 km West, 4 km South
Track the net displacement on a 2D grid: South is -Y, North is +Y, East is +X, West is -X. After all turns, sum the X and Y coordinates to find the displacement vector.
Track the net displacement on a 2D grid: South is -Y, North is +Y, East is +X, West is -X. After all turns, sum the X and Y coordinates to find the displacement vector.
Step 1: Plot the route from A
Start at (0,0). Move 6 km South: (0, -6). Take left turn (now facing East), move 4 km: (4, -6). Take another left turn (now facing North), move 6 km: (4, 0).
Step 2: Reach point B
From (4, 0), take a final right turn (now facing East), move 4 km: (8, 0). Point B is at (8, 0).
Step 3: Find distance and direction to A
To return from (8, 0) back to (0, 0), one must move 8 units in the negative X direction (West). Thus, the shortest distance is 8 km West.
A: 6 km West is incorrect as total displacement is 8 km; B: 6 km South is incorrect; C: 4 km West is incorrect as it ignores the total horizontal displacement of 8 km.
D is correct because by tracking the coordinate shifts (South 6km, Left 4km East, Left 6km North, Right 4km East), the final position relative to A is 8 km East; therefore, returning to A requires moving 8 km West.
In direction problems, always maintain a consistent coordinate plane where North/South is Y and East/West is X. This converts spatial visual puzzles into simple arithmetic.
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