Find the Distance Between Two Points (-7,-7) and (1,-3)

$(- 7, - 7)$ and $(1, - 3)$

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.

$\sqrt{{(1 - (- 7))}^{2} + {((- 3) - (- 7))}^{2}}$

Simplify.

Multiply $- 1$ by $- 7$ .

$\sqrt{{(1 + 7)}^{2} + {((- 3) - (- 7))}^{2}}$

Add $1$ and $7$ .

$\sqrt{8^{2} + {((- 3) - (- 7))}^{2}}$

Raise $8$ to the power of $2$ .

$\sqrt{64 + {((- 3) - (- 7))}^{2}}$

Multiply $- 1$ by $- 7$ .

$\sqrt{64 + {(- 3 + 7)}^{2}}$

Add $- 3$ and $7$ .

$\sqrt{64 + 4^{2}}$

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

$\sqrt{64 + 16}$

Add $64$ and $16$ .

$\sqrt{80}$

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5)}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 5}$

Pull terms out from under the radical.

$4 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{5}$

Decimal Form:

$8.94427190 \dots$