Whenever we need to find the distance of two point we are looking for the hypotenuse of a right triangle.
We need to use the Pythagorean Theorem to find the hypotenuse.
The Pythagorean Theorem is:
This applies to only to right triangles. a and b are the side lengths of the legs while c is the length of the hypotenuse.
In a Cartesian plane the side lengths a and b are represented like this:
So the Pythagorean Theorem would be:
We substitute the values to the Pythagorean theorem:
The distance between the points cannot be negative so only the positive square root is considered. Therefore the distance between the points is