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A person walks 12 km towards the west, turns left and walks 9 km. What is the shortest distance between his starting point and his current position?
15 km
21 km
12 km
10 km
15 km
Recognize the 3-4-5 Pythagorean triplet scaled by a factor of 3 (3x4=12, 3x3=9, so 3x5=15).
Recognize the 3-4-5 Pythagorean triplet scaled by a factor of 3 (3x4=12, 3x3=9, so 3x5=15).
Visualize Movement
Starting at the origin (0,0), the person moves 12 km West (-12, 0), then turns left (South) to move 9 km (-12, -9).
Apply Pythagoras Theorem
The distance squared is the sum of the squares of the horizontal and vertical displacements: 12 squared + 9 squared = 144 + 81 = 225. The square root of 225 is 15.
B: 21 km is the sum of the paths, not the shortest distance; C: 12 km ignores the vertical movement; D: 10 km is a miscalculation of the hypotenuse.
A is correct because the shortest distance forms the hypotenuse of a right-angled triangle with sides 12 km and 9 km, calculated as sqrt(12┬▓ + 9┬▓) = 15 km.
Always look for Pythagorean triplets (3-4-5, 5-12-13, 8-15-17) in direction problems to avoid manual calculation; doubling or tripling these sets is common in competitive exams.
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