geometry
"We use different formulas to find the distance of a segment on a number line, d=a−b" role="presentation" style="display: inline; fontsize: 16px; position: relative;">d=a−b, and the distance of a segment in the coordinate plane, d=(x2−x1)2+(y2−y1)2" role="presentation" style="display: inline; fontsize: 16px; position: relative;">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?"

values on the number line can be measured in either direction. So, it makes a difference which one is subtracted. The distance though, is always positive.
In the xy distance formula, the differences are squared, so that always gives a positive result.
If you think about it, the same formula would work on the number line.
d = √(x1x2)^2
will always give a positive result.posted by Steve
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