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

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

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.

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

Simplify.

Multiply $- 1$ by $- 3$ .

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

Add $- 9$ and $3$ .

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

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

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

Subtract $6$ from $- 2$ .

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

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.

$10$