Find the Distance Between Two Points (-9,3) and (-3,-5)

$(- 9, 3)$ and $(- 3, - 5)$

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.

$\sqrt{{((- 3) - (- 9))}^{2} + {((- 5) - 3)}^{2}}$

Simplify.

Multiply $- 1$ by $- 9$ .

$\sqrt{{(- 3 + 9)}^{2} + {((- 5) - 3)}^{2}}$

Add $- 3$ and $9$ .

$\sqrt{6^{2} + {((- 5) - 3)}^{2}}$

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

$\sqrt{36 + {((- 5) - 3)}^{2}}$

Subtract $3$ from $- 5$ .

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

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.

$10$