The Distance Formula
Consider the points (x1, y1) and (x2, y2) as shown in
the figure below.
The distance between
these points is the length of the hypotenuse of a right triangle as shown in the figure.
The length of side a is y2 - y1 and the length of side b is
x2 - x1. Using the
Pythagorean theorem, we can write
d2 = (x2 - x1)2 + (y2
If we apply the even-root property and omit the negative square root (because the
distance is positive), we can express this formula as follows.
The distance d between (x1, y1) and (x2, y2) is given by the formula
Using the distance formula
Find the length of the line segment with endpoints (-8, -10) and (6, -4).
Let (x1, y1) = (-8, -10) and (x2, y2)
= (6, -4). Now substitute the appropriate
values into the distance formula:
The exact length of the segment is