What Is the Distance Formula?


Quick Answer

The distance formula indicates that distance is equal to the square root of {x(sub 2) - x(sub 1)} (squared) + {y (sub 2) - y (sub 1)} (squared). The "x" and "y" values reflect the respective horizontal and vertical coordinates of each point on a graph; the formula is used to compute the distance between the two points.

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Full Answer

For example, students can imagine an exam question that asks for the distance between points with coordinates (-2, 1) and (1, 5) on Graph A. The first step is to assign the proper "x" and "y" values to each coordinate. In this case, x (sub1) = -2, y (sub1) = 1, x (sub2) = 1 and y (sub2) = 5.

The formula shows that distance equals the square root of {-3 - (-1)} (squared) + {5 - (-2)} (squared), further reducing to (-2) (squared) + 7 (squared), or, the square root of 4 plus 49, which is 53. Therefore, the distance between the points is the square root of 53, which is approximately equal to 7.28.

It does not matter which point is denoted the first {x (sub1), y (sub 1)} or second {x (sub2), y (sub2)} in the formula. However, it is important not to mismatch x- and y-values to avoid an incorrect calculation.

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