Find the Distance Between Two Points (3,-4) and (9,4)

$(3, - 4)$ and $(9, 4)$

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.

$\sqrt{{(9 - 3)}^{2} + {(4 - (- 4))}^{2}}$

Simplify.

Subtract $3$ from $9$ .

$\sqrt{6^{2} + {(4 - (- 4))}^{2}}$

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

$\sqrt{36 + {(4 - (- 4))}^{2}}$

Multiply $- 1$ by $- 4$ .

$\sqrt{36 + {(4 + 4)}^{2}}$

Add $4$ and $4$ .

$\sqrt{36 + 8^{2}}$

Raise $8$ to the power of $2$ .

$\sqrt{36 + 64}$

Add $36$ and $64$ .

$\sqrt{100}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2}}$

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

$10$