# 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 yA means the y-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:

## Examples

### Example 1

 Fill in the values:

### Example 2

It doesn't matter what order the points are in, because squaring removes any negatives:

 Fill in the values:

### Example 3

And here is another example with some negative coordinates ... it all still works:

 Fill in the values:

(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: