Why do you need absolute values when you write expressions for the lengths

of the legs, but not when you write the relationship in terms of the

Pythagorean Theorem?

Explanation:

Lengths are always positive.

Each leg is a one dimensional figure. The legs are perpendicular. You can draw one leg horizontally and the other leg vertically.

The length of the horizontal leg is just the difference of the x-coordinates of the end points. In order to not worry about the order of the coordinates you can subtract in any order but you have to take the absolute value to make sure the difference is positve.

The same is true for the vertical leg: find the difference of the y coordinates of the end points, and take the absolute value to make sure the result is positive.

When, you use the Pythagorean theorem, the lengths are squared. Thus, the value will aways be positive, regardless the order of the coordinates in your subtraction.

4 + 5 7/9= 9 7/9

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