The Distance Formula

Points A and B have coordinates (2, 3) and (5, 7).  The distance from point A to point B is the length of segment AB.  You can find that distance by drawing a right triangle, finding the lengths of its legs, and then using the Pythagorean Theorem:

 

Notice that the horizontal leg's length can be found by subtracting the x-coordinates of the points and the vertical leg's length can be found by subtracting the y-coordinates of the points.  In general, if the points have coordinates (x₁, y₁) and (x₂, y₂), then the distance d between them can be found by the Pythagorean Theorem:

or

Example: 

Find the length of segment CD if the coordinates of C are (–4, 7) and the coordinates of D are (2, 3).

Solution:

 

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