Find the Distance Between Two Points (-8,1) and (-4,-5)

$(- 8, 1)$ and $(- 4, - 5)$

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.

$\sqrt{{((- 4) - (- 8))}^{2} + {((- 5) - 1)}^{2}}$

Simplify.

Multiply $- 1$ by $- 8$ .

$\sqrt{{(- 4 + 8)}^{2} + {((- 5) - 1)}^{2}}$

Add $- 4$ and $8$ .

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

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

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

Subtract $1$ from $- 5$ .

$\sqrt{16 + {(- 6)}^{2}}$

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

$\sqrt{16 + 36}$

Add $16$ and $36$ .

$\sqrt{52}$

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

$\sqrt{4 (13)}$

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

$\sqrt{2^{2} \cdot 13}$

Pull terms out from under the radical.

$2 \sqrt{13}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{13}$

Decimal Form:

$7.21110255 \dots$