# Distance between Two Points Calculator

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

## Your Input

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

## Solution

The distance between two points $$$P = \left(p_{x}, p_{y}\right)$$$ and $$$Q = \left(q_{x}, q_{y}\right)$$$ is $$$d = \sqrt{\left(q_{x} - p_{x}\right)^{2} + \left(q_{y} - p_{y}\right)^{2}}$$$.

We have that $$$p_{x} = -2$$$, $$$p_{y} = 3$$$, $$$q_{x} = 5$$$, $$$q_{y} = 1$$$.

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