Find the Distance Between Two Points (0,-5) and (6,1)

$(0, - 5)$ and $(6, 1)$

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Substitute the actual values of the points into the distance formula.

$\sqrt{{(6 - 0)}^{2} + {(1 - (- 5))}^{2}}$

Simplify.

Subtract $0$ from $6$ .

$\sqrt{6^{2} + {(1 - (- 5))}^{2}}$

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

$\sqrt{36 + {(1 - (- 5))}^{2}}$

Multiply $- 1$ by $- 5$ .

$\sqrt{36 + {(1 + 5)}^{2}}$

Add $1$ and $5$ .

$\sqrt{36 + 6^{2}}$

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

$\sqrt{36 + 36}$

Add $36$ and $36$ .

$\sqrt{72}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2)}$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 2}$

Pull terms out from under the radical.

$6 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{2}$

Decimal Form:

$8.48528137 \dots$