In Figure
1 ,
A is (2,2),
B is (5,2), and
C is (5,6).
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Figure 1
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The distance formula.
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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 the hypotenuse. Therefore, by the Pythagorean theorem,
If
A is represented by the ordered pair (
x1,
y1) and
C is represented by the ordered pair (
x2,
y2), then
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
Linear Sentences in One Variable
Segments, Lines, and Inequalities
