Find the Distance Between Two Points (-4,-5) and (2,5)

$(- 4, - 5)$ and $(2, 5)$

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.

$\sqrt{{(2 - (- 4))}^{2} + {(5 - (- 5))}^{2}}$

Simplify.

Multiply $- 1$ by $- 4$ .

$\sqrt{{(2 + 4)}^{2} + {(5 - (- 5))}^{2}}$

Add $2$ and $4$ .

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

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

$\sqrt{36 + {(5 - (- 5))}^{2}}$

Multiply $- 1$ by $- 5$ .

$\sqrt{36 + {(5 + 5)}^{2}}$

Add $5$ and $5$ .

$\sqrt{36 + 10^{2}}$

Raise $10$ to the power of $2$ .

$\sqrt{36 + 100}$

Add $36$ and $100$ .

$\sqrt{136}$

Rewrite $136$ as $2^{2} \cdot 34$ .

Factor $4$ out of $136$ .

$\sqrt{4 (34)}$

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

$\sqrt{2^{2} \cdot 34}$

Pull terms out from under the radical.

$2 \sqrt{34}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{34}$

Decimal Form:

$11.66190378 \dots$