Distance Between Two Points



Distance between two 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)

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: c = square root of [(xA-xB)^2+(yA-yB)^2]

Examples

Proportional division of a line (section formula)