Find the Distance Between Two Points (-9,-2) and (-1,0)

$(- 9, - 2)$ and $(- 1, 0)$

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.

$\sqrt{{((- 1) - (- 9))}^{2} + {(0 - (- 2))}^{2}}$

Simplify.

Multiply $- 1$ by $- 9$ .

$\sqrt{{(- 1 + 9)}^{2} + {(0 - (- 2))}^{2}}$

Add $- 1$ and $9$ .

$\sqrt{8^{2} + {(0 - (- 2))}^{2}}$

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

$\sqrt{64 + {(0 - (- 2))}^{2}}$

Multiply $- 1$ by $- 2$ .

$\sqrt{64 + {(0 + 2)}^{2}}$

Add $0$ and $2$ .

$\sqrt{64 + 2^{2}}$

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

$\sqrt{64 + 4}$

Add $64$ and $4$ .

$\sqrt{68}$

Rewrite $68$ as $2^{2} \cdot 17$ .

Factor $4$ out of $68$ .

$\sqrt{4 (17)}$

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

$\sqrt{2^{2} \cdot 17}$

Pull terms out from under the radical.

$2 \sqrt{17}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{17}$

Decimal Form:

$8.24621125 \dots$