Find the Distance Between Two Points (-5,-4) , (7,-10)

$(- 5, - 4)$ , $(7, - 10)$

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.

$\sqrt{{(7 - (- 5))}^{2} + {((- 10) - (- 4))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 5$ .

$\sqrt{{(7 + 5)}^{2} + {((- 10) - (- 4))}^{2}}$

Add $7$ and $5$ .

$\sqrt{12^{2} + {((- 10) - (- 4))}^{2}}$

Raise $12$ to the power of $2$ .

$\sqrt{144 + {((- 10) - (- 4))}^{2}}$

Multiply $- 1$ by $- 4$ .

$\sqrt{144 + {(- 10 + 4)}^{2}}$

Add $- 10$ and $4$ .

$\sqrt{144 + {(- 6)}^{2}}$

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

$\sqrt{144 + 36}$

Add $144$ and $36$ .

$\sqrt{180}$

Rewrite $180$ as $6^{2} \cdot 5$ .

Factor $36$ out of $180$ .

$\sqrt{36 (5)}$

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

$\sqrt{6^{2} \cdot 5}$

Pull terms out from under the radical.

$6 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{5}$

Decimal Form:

$13.41640786 \dots$

Step 5