Distance Between 2 Points

Here is how to calculate the distance between two points when you know their coordinates:

graph 2 points

 

Let us call the two points A and B

 

graph 2 points

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

 

graph 2 points

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)

 

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:   graph 2 points

Examples

Example 1

graph 2 points

 

Fill in the values:   graph 2 points
     
graph 2 points

Example 2

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

graph 2 points

 

Fill in the values:   graph 2 points
     
graph 2 points

Example 3

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

graph 2 points

 

Fill in the values:   graph 2 points
     
graph 2 points

(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: