Distance Formula
In Figure 1,
A has coordinates (2,2),
B has coordinates (5,2), and
C has coordinates (5,6).
To find the length of
AB or
BC, only simple subtraction is necessary.
To find the length of
AC, however, simple subtraction is not sufficient. Triangle
ABC is a right triangle with
AC being the hypotenuse. Therefore, by the Pythagorean theorem,
From the Pythagorean theorem, we derive the distance formula, which is nothing more than a different format for the former. If
A is represented by the ordered pair (
x1 ,y1) and
C is represented by the ordered pair (
x2 ,y2), then
Then
d in the preceding formula stands for distance.
Example 1
Use the distance formula to find the distance between the points with coordinates (–3,4) and (5,2).
Let (–3,4) = (
x1 ,y1) and (5,2) = (
x2 ,y2). Then
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Posted by Muhammad Atif Saeed
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By Muhammad Atif Saeed
on 00:45. Filed under
Mathandstat
.
Follow any responses to the RSS 2.0. Leave a response
