Find the Distance Between Two Points (-5,-6) , (-3,-8)

$(- 5, - 6)$ , $(- 3, - 8)$

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.

$\sqrt{{((- 3) - (- 5))}^{2} + {((- 8) - (- 6))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 5$ .

$\sqrt{{(- 3 + 5)}^{2} + {((- 8) - (- 6))}^{2}}$

Add $- 3$ and $5$ .

$\sqrt{2^{2} + {((- 8) - (- 6))}^{2}}$

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

$\sqrt{4 + {((- 8) - (- 6))}^{2}}$

Multiply $- 1$ by $- 6$ .

$\sqrt{4 + {(- 8 + 6)}^{2}}$

Add $- 8$ and $6$ .

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

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

$\sqrt{4 + 4}$

Add $4$ and $4$ .

$\sqrt{8}$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2)}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 2}$

Pull terms out from under the radical.

$2 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$

Step 5