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

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

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.

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

Simplify.

Subtract $7$ from $5$ .

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

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

$\sqrt{4 + {(9 - (- 1))}^{2}}$

Multiply $- 1$ by $- 1$ .

$\sqrt{4 + {(9 + 1)}^{2}}$

Add $9$ and $1$ .

$\sqrt{4 + 10^{2}}$

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

$\sqrt{4 + 100}$

Add $4$ and $100$ .

$\sqrt{104}$

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:

$10.19803902 \dots$