Find the Distance Between Two Points (3,-1) , (-6,-7)

$(3, - 1)$ , $(- 6, - 7)$

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.

$\sqrt{{((- 6) - 3)}^{2} + {((- 7) - (- 1))}^{2}}$

Step 3

Simplify.

Subtract $3$ from $- 6$ .

$\sqrt{{(- 9)}^{2} + {((- 7) - (- 1))}^{2}}$

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

$\sqrt{81 + {((- 7) - (- 1))}^{2}}$

Multiply $- 1$ by $- 1$ .

$\sqrt{81 + {(- 7 + 1)}^{2}}$

Add $- 7$ and $1$ .

$\sqrt{81 + {(- 6)}^{2}}$

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

$\sqrt{81 + 36}$

Add $81$ and $36$ .

$\sqrt{117}$

Rewrite $117$ as $3^{2} \cdot 13$ .

Factor $9$ out of $117$ .

$\sqrt{9 (13)}$

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

$\sqrt{3^{2} \cdot 13}$

Pull terms out from under the radical.

$3 \sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{13}$

Decimal Form:

$10.81665382 \dots$

Step 5