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=(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

Distances are considered to be non-negative in all cases.

The absolute value function is necessary to get a positive result when the difference of coordinate values is negative.

The square root function is defined to return a positive result always, so no absolute value function is required when the distance is found using the square root function.