Find the Distance Between Two Points (-1,3) , (11,-2)

$(- 1, 3)$ , $(11, - 2)$

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.

$\sqrt{{(11 - (- 1))}^{2} + {((- 2) - 3)}^{2}}$

Simplify.

Multiply $- 1$ by $- 1$ .

$\sqrt{{(11 + 1)}^{2} + {((- 2) - 3)}^{2}}$

Add $11$ and $1$ .

$\sqrt{12^{2} + {((- 2) - 3)}^{2}}$

Raise $12$ to the power of $2$ .

$\sqrt{144 + {((- 2) - 3)}^{2}}$

Subtract $3$ from $- 2$ .

$\sqrt{144 + {(- 5)}^{2}}$

Raise $- 5$ to the power of $2$ .

$\sqrt{144 + 25}$

Add $144$ and $25$ .

$\sqrt{169}$

Rewrite $169$ as $13^{2}$ .

$\sqrt{13^{2}}$

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

$13$