Find the Distance Between Two Points (-5,-4) , (-3,2)

$(- 5, - 4)$ , $(- 3, 2)$

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.

$\sqrt{{((- 3) - (- 5))}^{2} + {(2 - (- 4))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 5$ .

$\sqrt{{(- 3 + 5)}^{2} + {(2 - (- 4))}^{2}}$

Add $- 3$ and $5$ .

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

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

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

Multiply $- 1$ by $- 4$ .

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

Add $2$ and $4$ .

$\sqrt{4 + 6^{2}}$

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

$\sqrt{4 + 36}$

Add $4$ and $36$ .

$\sqrt{40}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$\sqrt{4 (10)}$

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

$\sqrt{2^{2} \cdot 10}$

Pull terms out from under the radical.

$2 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{10}$

Decimal Form:

$6.32455532 \dots$

Step 5