Find the Distance Between Two Points (-3,-3) and (-6,1)

$(- 3, - 3)$ and $(- 6, 1)$

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.

$\sqrt{{((- 6) - (- 3))}^{2} + {(1 - (- 3))}^{2}}$

Simplify.

Multiply $- 1$ by $- 3$ .

$\sqrt{{(- 6 + 3)}^{2} + {(1 - (- 3))}^{2}}$

Add $- 6$ and $3$ .

$\sqrt{{(- 3)}^{2} + {(1 - (- 3))}^{2}}$

Raise $- 3$ to the power of $2$ .

$\sqrt{9 + {(1 - (- 3))}^{2}}$

Multiply $- 1$ by $- 3$ .

$\sqrt{9 + {(1 + 3)}^{2}}$

Add $1$ and $3$ .

$\sqrt{9 + 4^{2}}$

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

$\sqrt{9 + 16}$

Add $9$ and $16$ .

$\sqrt{25}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2}}$

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

$5$