Find the Distance Between Two Points (6,-1) and (0,7)

$(6, - 1)$ and $(0, 7)$

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.

$\sqrt{{(0 - 6)}^{2} + {(7 - (- 1))}^{2}}$

Simplify.

Subtract $6$ from $0$ .

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

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

$\sqrt{36 + {(7 - (- 1))}^{2}}$

Multiply $- 1$ by $- 1$ .

$\sqrt{36 + {(7 + 1)}^{2}}$

Add $7$ 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.

$10$