Deriving the Distance Formula from the Pythagorean Theorem Date:
03/23/2003 at 05:14:57 From: Hans Subject: Formula derivation
How does one derive the distance formula from the Pythagorean
theorem? Thanks. Date: 03/23/2003 at 09:23:14 From: Doctor Jerry
Subject: Re: Formula derivation Hi Hans, Suppose we have points
(x1,y1) and (x2,y2) in the (x,y)-plane. To keep things simple,
let's suppose that (x2,y2) is upward and to the right of
(x1,y1). From (x1,y1) draw a horizontal line to the right,
stopping just below (x2,y2). From (x2,y2) draw a vertical line
downward, stopping at (x2,y1), where it touches the first line.
Now draw a line connecting (x1,y1) and (x2,y2). You will see on
your paper a right triangle, with right angle at (x2,y1). The
lengths of the sides of this right triangle are x2-x1 and y2-y1.
So, the length d of the hypotenuse is (by the Pythagorean
theorem) d^2 = (x2-x1)^2 + (y2-y1)^2. Now all you have to do is
to take the positive square root of both sides. - Doctor Jerry,
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