Find the Distance Between Two Points (9,9) and (6,5)

$(9, 9)$ and $(6, 5)$

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.

$\sqrt{{(6 - 9)}^{2} + {(5 - 9)}^{2}}$

Simplify.

Subtract $9$ from $6$ .

$\sqrt{{(- 3)}^{2} + {(5 - 9)}^{2}}$

Raise $- 3$ to the power of $2$ .

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

Subtract $9$ from $5$ .

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

Raise $- 4$ to the power of $2$ .

$\sqrt{9 + 16}$

Add $9$ and $16$ .

$\sqrt{25}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$5$