Find the Distance Between Two Points (-2,-1) , (-8,-7)

$(- 2, - 1)$ , $(- 8, - 7)$

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.

$\sqrt{{((- 8) - (- 2))}^{2} + {((- 7) - (- 1))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 2$ .

$\sqrt{{(- 8 + 2)}^{2} + {((- 7) - (- 1))}^{2}}$

Add $- 8$ and $2$ .

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

Raise $- 6$ to the power of $2$ .

$\sqrt{36 + {((- 7) - (- 1))}^{2}}$

Multiply $- 1$ by $- 1$ .

$\sqrt{36 + {(- 7 + 1)}^{2}}$

Add $- 7$ and $1$ .

$\sqrt{36 + {(- 6)}^{2}}$

Raise $- 6$ to the power of $2$ .

$\sqrt{36 + 36}$

Add $36$ and $36$ .

$\sqrt{72}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2)}$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 2}$

Pull terms out from under the radical.

$6 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{2}$

Decimal Form:

$8.48528137 \dots$

Step 5