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

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

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.

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

Simplify.

Subtract $6$ from $- 1$ .

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

Raise $- 7$ to the power of $2$ .

$\sqrt{49 + {(6 - (- 1))}^{2}}$

Multiply $- 1$ by $- 1$ .

$\sqrt{49 + {(6 + 1)}^{2}}$

Add $6$ and $1$ .

$\sqrt{49 + 7^{2}}$

Raise $7$ to the power of $2$ .

$\sqrt{49 + 49}$

Add $49$ and $49$ .

$\sqrt{98}$

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$\sqrt{49 (2)}$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} \cdot 2}$

Pull terms out from under the radical.

$7 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{2}$

Decimal Form:

$9.89949493 \dots$