geometry
posted by jill
"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?"

Steve
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.
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