Why is it necessary to use the absolute value of the difference when finding the distance on a number line, but not necessary when finding the differences of

Question

We use different formulas to find the distance of a segment on a number line, d = |a−b|, and the distance of a segment in the coordinate plane, d = sqrt [(x2−x1)^2+(y2−y1)^2]. Why is it necessary to use the absolute value of the difference when finding the distance on a number line, but not necessary when finding the differences of the coordinates in the coordinate plane?

Answer 1

 

    Believe it or not it's pretty much the same thing

 

   | x - y | =  sqrt [  (x-y)^2 |