Shortest path calculation using Pythagoras theorem The Pythagoras theorem states that in a right triangle, the square of the shortest side (a) is equal...
Shortest path calculation using Pythagoras theorem
The Pythagoras theorem states that in a right triangle, the square of the shortest side (a) is equal to the sum of the squares of the other two sides (b and c). In other words:
a^2 = b^2 + c^2
This theorem can be used to calculate the shortest path between two points in a coordinate plane by finding the square root of the sum of the squares of the differences between the coordinates of the two points.
How to use the Pythagorean theorem:
Identify the two points you are interested in finding the shortest path between.
Find the coordinates of the two points.
Calculate the difference between the coordinates of the two points.
Square the difference between the coordinates.
Add the squares of the two other side lengths together.
Take the square root of the sum of the squares of the differences between the coordinates.
That's the length of the shortest path between the two points.
Examples:
If you have two points at (2, 3) and (4, 6), the difference between the coordinates is 2. The squares of the differences between the coordinates are 2^2 = 4 and 4^2 = 16. Therefore, the total square is 4 + 16 = 20. The shortest path length between these two points is sqrt(20) = 2sqrt(5).
Another example would be finding the shortest path between (0, 0) and (10, 10). The difference between the coordinates is 10, and the squares of these differences are 10^2 = 100 and 10^2 = 100. Therefore, the total square is 100 + 100 = 200. The shortest path length between these two points is sqrt(200) = 2sqrt(10)