Maths Olympiad Prep

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Geometry Difficulty 3.6 AMC 10/12 Find the answer South Africa

A hiker walks 11 km East, then 22 km North, then 33 km West, then 44 km South, then 55 km East and finally 66 km North. The hiker's straight-line distance in km from the starting point is

Pick one

Solution

Horizontal distance travelled:
1−3+5=3 (i.e. 3 km East) 1 - 3 + 5 = 3 \text{ (i.e. 3 km East)}
Vertical distance travelled:
2−4+6=4 (i.e. 4 km North) 2 - 4 + 6 = 4 \text{ (i.e. 4 km North)}
By Pythagoras, the straight-line distance from the starting point is thus 55 km.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.