Find the Distance Between Two Points (-1,7) and (9,5)

$(- 1, 7)$ and $(9, 5)$

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.

$\sqrt{{(9 - (- 1))}^{2} + {(5 - 7)}^{2}}$

Simplify.

Multiply $- 1$ by $- 1$ .

$\sqrt{{(9 + 1)}^{2} + {(5 - 7)}^{2}}$

Add $9$ and $1$ .

$\sqrt{10^{2} + {(5 - 7)}^{2}}$

Raise $10$ to the power of $2$ .

$\sqrt{100 + {(5 - 7)}^{2}}$

Subtract $7$ from $5$ .

$\sqrt{100 + {(- 2)}^{2}}$

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

$\sqrt{100 + 4}$

Add $100$ and $4$ .

$\sqrt{104}$

Rewrite $104$ as $2^{2} \cdot 26$ .

Factor $4$ out of $104$ .

$\sqrt{4 (26)}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 26}$

Pull terms out from under the radical.

$2 \sqrt{26}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{26}$

Decimal Form:

$10.19803902 \dots$