Find the Distance Between Two Points (13,9) , (11,15)

$(13, 9)$ , $(11, 15)$

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.

$\sqrt{{(11 - 13)}^{2} + {(15 - 9)}^{2}}$

Simplify.

Subtract $13$ from $11$ .

$\sqrt{{(- 2)}^{2} + {(15 - 9)}^{2}}$

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

$\sqrt{4 + {(15 - 9)}^{2}}$

Subtract $9$ from $15$ .

$\sqrt{4 + 6^{2}}$

Raise $6$ to the power of $2$ .

$\sqrt{4 + 36}$

Add $4$ and $36$ .

$\sqrt{40}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$\sqrt{4 (10)}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 10}$

Pull terms out from under the radical.

$2 \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{10}$

Decimal Form:

$6.32455532 \dots$