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Starting from point X, a cyclist travels 12 km North, turns East and travels 9 km, then turns South and travels 6 km, and finally turns West and travels 1 km. What is the shortest distance from the starting point?
10 km
12 km
8 km
9 km
10 km
Calculate net displacement by subtracting opposite vectors: Net North = 12 - 6 = 6 km; Net East = 9 - 1 = 8 km. Apply Pythagorean triplet (6, 8, 10).
Calculate net displacement by subtracting opposite vectors: Net North = 12 - 6 = 6 km; Net East = 9 - 1 = 8 km. Apply Pythagorean triplet (6, 8, 10).
Calculate Net Displacements
Starting at (0,0): Move North 12 km to (0, 12). Move East 9 km to (9, 12). Move South 6 km to (9, 12 - 6 = 6). Move West 1 km to (9 - 1 = 8, 6).
Apply Pythagoras Theorem
The coordinates relative to the start (0,0) are (8, 6). The shortest distance is the hypotenuse: square root of (8 squared + 6 squared) = square root of (64 + 36) = square root of 100 = 10 km.
B: 12 km is incorrect as it ignores the net change in both coordinates. C: 8 km fails to account for the North-South displacement. D: 9 km is a distractor based on simple subtraction without considering the triangle geometry.
A is correct because the net horizontal displacement is 8 km and vertical displacement is 6 km, forming a 6-8-10 Pythagorean triplet.
Whenever you see 4-direction movements, always calculate net North-South and East-West distances separately before finding the resultant using the square root of the sum of squares.