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Use coordinates with O = (0, 0), East as positive x and North as positive y. Horizontal calculation: the person moves 6 m East and 9 m West, so net x = 6 - 9 = -3 m. Vertical calculation: the person moves 10 m North and 6 m South, so net y = 10 - 6 = 4 m. The signs of (-3, 4) place the final point in the North-West direction. The shortest distance is straight-line displacement: √((-3)² + (4)²) = √(9 + 16) = √25 = 5 m. Therefore option B, North-West, 5 m, is correct. The opposite-direction option is wrong because it reverses the verified coordinate signs. The option giving 7 m is wrong because it does not use the Pythagorean shortest distance. The North option is wrong because both non-zero coordinate components, or the exact zero component, determine North-West, not a neighbouring compass direction.
FAQ
Common questions and clear answers for this topic.
Direction Test questions describe movements or turns and ask for the final direction, relative position or shortest distance from a starting point. They test compass knowledge, spatial tracking and displacement calculation.
Find net East-West movement as x and net North-South movement as y. The shortest distance from the start is √(x² + y²), while the signs of x and y determine the final compass direction.
Use coordinates: East +x, West -x, North +y and South -y. Add movements axis-wise, identify direction from the final signs and use the Pythagorean formula when both coordinates are non-zero.
