Find the Distance Between Two Points (-6,5) and (-3,1)

$(- 6, 5)$ and $(- 3, 1)$

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.

$\sqrt{{((- 3) - (- 6))}^{2} + {(1 - 5)}^{2}}$

Simplify.

Multiply $- 1$ by $- 6$ .

$\sqrt{{(- 3 + 6)}^{2} + {(1 - 5)}^{2}}$

Add $- 3$ and $6$ .

$\sqrt{3^{2} + {(1 - 5)}^{2}}$

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

$\sqrt{9 + {(1 - 5)}^{2}}$

Subtract $5$ from $1$ .

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

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.

$5$