Find the Distance Between Two Points (-9,4) and (-5,-6)

$(- 9, 4)$ and $(- 5, - 6)$

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.

$\sqrt{{((- 5) - (- 9))}^{2} + {((- 6) - 4)}^{2}}$

Simplify.

Multiply $- 1$ by $- 9$ .

$\sqrt{{(- 5 + 9)}^{2} + {((- 6) - 4)}^{2}}$

Add $- 5$ and $9$ .

$\sqrt{4^{2} + {((- 6) - 4)}^{2}}$

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

$\sqrt{16 + {((- 6) - 4)}^{2}}$

Subtract $4$ from $- 6$ .

$\sqrt{16 + {(- 10)}^{2}}$

Raise $- 10$ to the power of $2$ .

$\sqrt{16 + 100}$

Add $16$ and $100$ .

$\sqrt{116}$

Rewrite $116$ as $2^{2} \cdot 29$ .

Factor $4$ out of $116$ .

$\sqrt{4 (29)}$

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

$\sqrt{2^{2} \cdot 29}$

Pull terms out from under the radical.

$2 \sqrt{29}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{29}$

Decimal Form:

$10.77032961 \dots$