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A person walks 12 km towards West, then turns South and walks 3 km, then turns East and walks 8 km. How far is he from his starting point?
5 km
4 km
6 km
7 km
5 km
Calculate net displacement in X (West-East) and Y (North-South) axes, then apply the Pythagorean theorem: distance = sqrt(deltaX squared + deltaY squared).
Calculate net displacement in X (West-East) and Y (North-South) axes, then apply the Pythagorean theorem: distance = sqrt(deltaX squared + deltaY squared).
Analyze Horizontal and Vertical movements
Starting at origin (0,0), walking 12 km West means position becomes (-12, 0). Then 3 km South makes it (-12, -3). Finally, 8 km East moves it to (-12 + 8, -3), resulting in (-4, -3).
Apply Pythagoras Theorem
The distance from (0,0) to (-4, -3) is calculated as sqrt((-4)2 + (-3)2) = sqrt(16 + 9) = sqrt(25) = 5 km.
B: 4 km is mathematically incorrect as it ignores the vertical component of the displacement. C: 6 km is a common estimation error not supported by the calculation. D: 7 km results from incorrectly adding horizontal components rather than calculating vector displacement.
A is correct because the net displacement forms a right-angled triangle with sides of 4 km and 3 km, resulting in a hypotenuse of 5 km.
Always treat West/South as negative and East/North as positive on a coordinate grid to avoid sign errors when calculating net displacement.