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. x_A means the x-coordinate of point A y_A means the y-coordinate of point A The horizontal distance "a" is (x_A - x_B) The vertical distance "b" is (y_A - y_B)

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 = (x_A - x_B)² + (y_A - y_B)²

And the final result:

Examples

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)

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: