Find the Distance Between Two Points (12,-1) , (18,-9)

$(12, - 1)$ , $(18, - 9)$

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.

$\sqrt{{(18 - 12)}^{2} + {((- 9) - (- 1))}^{2}}$

Simplify.

Subtract $12$ from $18$ .

$\sqrt{6^{2} + {((- 9) - (- 1))}^{2}}$

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

$\sqrt{36 + {((- 9) - (- 1))}^{2}}$

Multiply $- 1$ by $- 1$ .

$\sqrt{36 + {(- 9 + 1)}^{2}}$

Add $- 9$ and $1$ .

$\sqrt{36 + {(- 8)}^{2}}$

Raise $- 8$ to the power of $2$ .

$\sqrt{36 + 64}$

Add $36$ and $64$ .

$\sqrt{100}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$10$