The distance formula and the Pythagorean theorem are really just the same thing. Recall that the Pythagorean theorem allowed you to calculate the hypotenuse, *c* of a right triangle from the lengths of the other two sides, *a* and *b*:

*c* = [*a*^{2}+*b*^{2}]^{1/2}

Think about a piece of graph paper. The *x* and *y* axes are always perpendicular, yes? So any line segment on that paper can be thought of as the hypotenuse of a right triangle, with the sides parallel to the *x* and *y* axes.

So the length of the line segment, *d*, is "the square root of the sum of the squares of the other two sides":

`
d=
[-)^{2} +
(-)^{2}]^{1/2} `

*d*=