Find the Distance Between Two Points (-2,-2) and (0,7)

$(- 2, - 2)$ and $(0, 7)$

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.

$\sqrt{{(0 - (- 2))}^{2} + {(7 - (- 2))}^{2}}$

Simplify.

Multiply $- 1$ by $- 2$ .

$\sqrt{{(0 + 2)}^{2} + {(7 - (- 2))}^{2}}$

Add $0$ and $2$ .

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

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

$\sqrt{4 + {(7 - (- 2))}^{2}}$

Multiply $- 1$ by $- 2$ .

$\sqrt{4 + {(7 + 2)}^{2}}$

Add $7$ and $2$ .

$\sqrt{4 + 9^{2}}$

Raise $9$ to the power of $2$ .

$\sqrt{4 + 81}$

Add $4$ and $81$ .

$\sqrt{85}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{85}$

Decimal Form:

$9.21954445 \dots$