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South African Mathematics Olympiad

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

A hiker walks $1$ km East, then $2$ km North, then $3$ km West, then $4$ km South, then $5$ km East and finally $6$ km North. The hiker's straight-line distance in km from the starting point is

Pick one

Solution

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

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