Find the Distance Between Two Points (13,2) and (7,10)

$(13, 2)$ and $(7, 10)$

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.

$\sqrt{{(7 - 13)}^{2} + {(10 - 2)}^{2}}$

Simplify.

Subtract $13$ from $7$ .

$\sqrt{{(- 6)}^{2} + {(10 - 2)}^{2}}$

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

$\sqrt{36 + {(10 - 2)}^{2}}$

Subtract $2$ from $10$ .

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

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.

$10$