Find the Distance Between Two Points (-2,-6) and (-7,6)

$(- 2, - 6)$ and $(- 7, 6)$

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.

$\sqrt{{((- 7) - (- 2))}^{2} + {(6 - (- 6))}^{2}}$

Simplify.

Multiply $- 1$ by $- 2$ .

$\sqrt{{(- 7 + 2)}^{2} + {(6 - (- 6))}^{2}}$

Add $- 7$ and $2$ .

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

Raise $- 5$ to the power of $2$ .

$\sqrt{25 + {(6 - (- 6))}^{2}}$

Multiply $- 1$ by $- 6$ .

$\sqrt{25 + {(6 + 6)}^{2}}$

Add $6$ and $6$ .

$\sqrt{25 + 12^{2}}$

Raise $12$ to the power of $2$ .

$\sqrt{25 + 144}$

Add $25$ and $144$ .

$\sqrt{169}$

Rewrite $169$ as $13^{2}$ .

$\sqrt{13^{2}}$

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

$13$