Find the Distance Between Two Points (-6,7) , (-1,-5)

$(- 6, 7)$ , $(- 1, - 5)$

Step 1

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

Substitute the actual values of the points into the distance formula.

$\sqrt{{((- 1) - (- 6))}^{2} + {((- 5) - 7)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 6$ .

$\sqrt{{(- 1 + 6)}^{2} + {((- 5) - 7)}^{2}}$

Add $- 1$ and $6$ .

$\sqrt{5^{2} + {((- 5) - 7)}^{2}}$

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

$\sqrt{25 + {((- 5) - 7)}^{2}}$

Subtract $7$ from $- 5$ .

$\sqrt{25 + {(- 12)}^{2}}$

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.

$13$

Step 4