Find the Distance Between Two Points (-5,-8) and (-1,-16)

$(- 5, - 8)$ and $(- 1, - 16)$

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.

$\sqrt{{((- 1) - (- 5))}^{2} + {((- 16) - (- 8))}^{2}}$

Simplify.

Multiply $- 1$ by $- 5$ .

$\sqrt{{(- 1 + 5)}^{2} + {((- 16) - (- 8))}^{2}}$

Add $- 1$ and $5$ .

$\sqrt{4^{2} + {((- 16) - (- 8))}^{2}}$

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

$\sqrt{16 + {((- 16) - (- 8))}^{2}}$

Multiply $- 1$ by $- 8$ .

$\sqrt{16 + {(- 16 + 8)}^{2}}$

Add $- 16$ and $8$ .

$\sqrt{16 + {(- 8)}^{2}}$

Raise $- 8$ to the power of $2$ .

$\sqrt{16 + 64}$

Add $16$ and $64$ .

$\sqrt{80}$

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5)}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 5}$

Pull terms out from under the radical.

$4 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{5}$

Decimal Form:

$8.94427190 \dots$