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:
a^{2} + b^{2} = c^{2}
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})
Now we can solve for c (the distance between the points):
Start with: | c^{2} = a^{2} + b^{2} | |
Put in the calculations for a and b: | c^{2} = (x_{A} − x_{B})^{2} + (y_{A} − y_{B})^{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)
Try It Yourself
Drag the points:
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 (8,2,6) and (3,5,7) is:
= √( (8−3)^{2} + (2−5)^{2} + (6−7)^{2} ) |
= √( 5^{2} + (−3)^{2} + (−1)^{2} ) |
= √( 25 + 9 + 1 ) |
= √35 |
Which is about 5.9 |