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A person walks 5 km East, turns South and walks 4 km, then turns West and walks 2 km. How far is he from the starting point?
5 km
7 km
3 km
4 km
5 km
Represent movements on a coordinate plane; calculate the net displacement using the Pythagorean theorem (root of [horizontal distance squared + vertical distance squared]).
Represent movements on a coordinate plane; calculate the net displacement using the Pythagorean theorem (root of [horizontal distance squared + vertical distance squared]).
Define Displacement Vectors
Set the starting point at (0, 0). Movement 1: East 5 km reaches (5, 0). Movement 2: South 4 km reaches (5, -4). Movement 3: West 2 km reaches (5-2, -4) which is (3, -4).
Calculate Net Distance
The final position is (3, -4). Distance from (0, 0) is calculated as square root of (3 squared + (-4) squared) = square root of (9 + 16) = square root of 25 = 5 km.
B: 7 km is incorrect because it is the sum of all movements, ignoring directionality. C: 3 km is incorrect because it ignores the vertical component of the path. D: 4 km is incorrect because it represents only the vertical displacement without considering the horizontal shift.
A is correct because the resultant displacement forms the hypotenuse of a right-angled triangle with base 3 km (5-2) and height 4 km, calculating to 5 km via the Pythagoras theorem.
Always track the X and Y coordinates separately; treating direction problems as coordinate geometry prevents errors caused by misinterpreting turns.
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