Distance between Two Points Calculator

For two given points, the calculator will find the distance between them, with steps shown.

$$$($$$ $$$)$$$
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$$$($$$ $$$)$$$
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Your Input

Find the distance between $$$P = \left(-2, 3\right)$$$ and $$$Q = \left(5, 1\right)$$$.

Solution

The distance between two points $$$P$$$ and $$$Q$$$ is $$$d = \sqrt{\sum_{i=1}^{n} \left(q_{i} - p_{i}\right)^{2}}$$$ ($$$n$$$ is the number of coordinates of each of the two points, $$$p_i, i=\overline{1..n}$$$ and $$$q_i, i=\overline{1..n}$$$ are the coordinates of the first and the second points respectively).

Thus, $$$d = \sqrt{\left(5 - \left(-2\right)\right)^{2} + \left(1 - 3\right)^{2}} = \sqrt{53}$$$.

Answer

$$$d = \sqrt{53}\approx 7.280109889280518$$$A