Whenever we need to find the distance of two point we are looking for the hypotenuse of a right triangle.
The Pythagorean Theorem states that:
The Pythagorean Theorem applies to right triangles only. 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:
as the coordinates of her house or
as the coordinates of her school or
We substitute the values to the Pythagorean theorem:
c cannot be negative since it is a side length.
Therefore the hypotenuse is