The distance between two points on a plane can be found by Pythagoras's theorem.
The shortest route from her home to her workplace is the route that passes along the block in the middle of the graph ,which is approximately 2.5 blocks shorter, than the apparently next shortest route.
Reason:
The shortest distance between two points is a straight line.
The shortest route to her workplace are the routes that approximate a straight line the most.
Following the dotted lines, there are two routes, that are approximately direct and therefore short routes to her workplace which are;
- The route heading past the block close to the center of the map to her workplace
- The route to the left of the above route
Taking the route that passes close to the center of the map to her workplace ,gives;
Path 1 = √(2² + 4²) = 2·√5 (by Pythagoras's theorem)
Path 2 = √(1² + 2²) = √5
Path 3 = 1 + 1 = 2
Path 4 = √(2² + 3²) = √13
Path 5 = 3
Cumulative distance = 2·√5 + √5 + 2 + √13 + 3 ≈ 15.3
Taking the route to the left of the above route, gives;
Path 1 = √(2² + 4²) = 2·√5
Path 2 = 7 + 6 = 13
Cumulative distance = 2·√5 + 13 ≈ 17.5
Therefore, the shortest route is the route that heads to her workplace, through, close to the center of the map, which approximately 17.5 blocks - 15.3 blocks = 2.5 blocks shorter
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