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The Distance Formula

In analytic geometry, the distance between two points of the xy-plane can be found using the distance formula. Distance Formula is used to calculate the distance between two points. The distance between (x1, y1) and (x2, y2) is given by:The Distance Formula

\[\large d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\]

Example For The Distance Formula

Question: Given the points (-1, -2) and (-3, 5), find the distance between them.


Label the points as follows

$\left(x_{1},y_{1}\right)=\left(-1, -2\right) and \left(x_{2},y_{2}\right)=\left(-3, 5\right)$

Therefore: $x_{1}=-1,\: y_{1}=-2,\: x_{2}=-3, and\: y_{2}=5$

To find the distance (d) between the points, use the distance formula: