Find the Distance Between Two Points (-5,-3) , (-9,-6)

$(- 5, - 3)$ , $(- 9, - 6)$

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.

$\sqrt{{((- 9) - (- 5))}^{2} + {((- 6) - (- 3))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 5$ .

$\sqrt{{(- 9 + 5)}^{2} + {((- 6) - (- 3))}^{2}}$

Add $- 9$ and $5$ .

$\sqrt{{(- 4)}^{2} + {((- 6) - (- 3))}^{2}}$

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

$\sqrt{16 + {((- 6) - (- 3))}^{2}}$

Multiply $- 1$ by $- 3$ .

$\sqrt{16 + {(- 6 + 3)}^{2}}$

Add $- 6$ and $3$ .

$\sqrt{16 + {(- 3)}^{2}}$

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

$\sqrt{16 + 9}$

Add $16$ and $9$ .

$\sqrt{25}$

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

$\sqrt{5^{2}}$

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

$5$

Step 4