Distance Between 2 Points
Here is how to calculate the distance between two points when you know their coordinates:
|Let us call the two points A and B|
We can run lines down from A, and along from B, to make a Right Angled Triangle.
And with a little help from Pythagoras we know that:
a2 + b2 = c2
Now label the coordinates of points A and B.
xA means the x-coordinate of point A
The horizontal distance "a" is (xA - xB)
The vertical distance "b" is (yA - yB)
So now we can solve for c (the distance between the points):
|Start with:||c2 = a2 + b2|
|Put in the calculations for a and b:||c2 = (xA - xB)2 + (yA - yB)2|
|And the final result:|
It doesn't matter what order the points are in, because squaring removes any negatives:
And here is another example with some negative coordinates ... it all still works:
(Note √136 can be further simplified to 2√34 if you want)
Three or More Dimensions
It works perfectly well in 3 (or more dimensions) !
Square the difference for each axis, then sum them up and take the square root:
The distance between the two points (9,2,7) and (4,8,10) is: