Find the Distance Between Two Points (-9,8) and (-3,-1)

$(- 9, 8)$ and $(- 3, - 1)$

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.

$\sqrt{{((- 3) - (- 9))}^{2} + {((- 1) - 8)}^{2}}$

Simplify.

Multiply $- 1$ by $- 9$ .

$\sqrt{{(- 3 + 9)}^{2} + {((- 1) - 8)}^{2}}$

Add $- 3$ and $9$ .

$\sqrt{6^{2} + {((- 1) - 8)}^{2}}$

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

$\sqrt{36 + {((- 1) - 8)}^{2}}$

Subtract $8$ from $- 1$ .

$\sqrt{36 + {(- 9)}^{2}}$

Raise $- 9$ to the power of $2$ .

$\sqrt{36 + 81}$

Add $36$ and $81$ .

$\sqrt{117}$

Rewrite $117$ as $3^{2} \cdot 13$ .

Factor $9$ out of $117$ .

$\sqrt{9 (13)}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 13}$

Pull terms out from under the radical.

$3 \sqrt{13}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{13}$

Decimal Form:

$10.81665382 \dots$