Find the Distance Between Two Points (-7,-3) , (-4,3)

$(- 7, - 3)$ , $(- 4, 3)$

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.

$\sqrt{{((- 4) - (- 7))}^{2} + {(3 - (- 3))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 7$ .

$\sqrt{{(- 4 + 7)}^{2} + {(3 - (- 3))}^{2}}$

Add $- 4$ and $7$ .

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

Raise $3$ to the power of $2$ .

$\sqrt{9 + {(3 - (- 3))}^{2}}$

Multiply $- 1$ by $- 3$ .

$\sqrt{9 + {(3 + 3)}^{2}}$

Add $3$ and $3$ .

$\sqrt{9 + 6^{2}}$

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

$\sqrt{9 + 36}$

Add $9$ and $36$ .

$\sqrt{45}$

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$\sqrt{9 (5)}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 5}$

Pull terms out from under the radical.

$3 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5}$

Decimal Form:

$6.70820393 \dots$

Step 5