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Distance Formula

In Figure 1 , A is (2,2), B is (5,2), and C is (5,6).





Figure 1

The distance formula.


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




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