Find the Distance Between Two Points (1,4) , (5,1)

$(1, 4)$ , $(5, 1)$

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Substitute the actual values of the points into the distance formula.

$\sqrt{{(5 - 1)}^{2} + {(1 - 4)}^{2}}$

Simplify.

Subtract $1$ from $5$ .

$\sqrt{4^{2} + {(1 - 4)}^{2}}$

Raise $4$ to the power of $2$ .

$\sqrt{16 + {(1 - 4)}^{2}}$

Subtract $4$ from $1$ .

$\sqrt{16 + {(- 3)}^{2}}$

Raise $- 3$ to the power of $2$ .

$\sqrt{16 + 9}$

Add $16$ and $9$ .

$\sqrt{25}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$5$