Find the Distance Between Two Points (-9,-2) and (-3,6)

$(- 9, - 2)$ and $(- 3, 6)$

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.

$\sqrt{{((- 3) - (- 9))}^{2} + {(6 - (- 2))}^{2}}$

Simplify.

Multiply $- 1$ by $- 9$ .

$\sqrt{{(- 3 + 9)}^{2} + {(6 - (- 2))}^{2}}$

Add $- 3$ and $9$ .

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

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

$\sqrt{36 + {(6 - (- 2))}^{2}}$

Multiply $- 1$ by $- 2$ .

$\sqrt{36 + {(6 + 2)}^{2}}$

Add $6$ and $2$ .

$\sqrt{36 + 8^{2}}$

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

$\sqrt{36 + 64}$

Add $36$ and $64$ .

$\sqrt{100}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$10$