Find the Distance Between Two Points (2,3) , (14,8)

$(2, 3)$ , $(14, 8)$

Step 1

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

Substitute the actual values of the points into the distance formula.

$\sqrt{{(14 - 2)}^{2} + {(8 - 3)}^{2}}$

Step 3

Simplify.

Subtract $2$ from $14$ .

$\sqrt{12^{2} + {(8 - 3)}^{2}}$

Raise $12$ to the power of $2$ .

$\sqrt{144 + {(8 - 3)}^{2}}$

Subtract $3$ from $8$ .

$\sqrt{144 + 5^{2}}$

Raise $5$ to the power of $2$ .

$\sqrt{144 + 25}$

Add $144$ and $25$ .

$\sqrt{169}$

Rewrite $169$ as $13^{2}$ .

$\sqrt{13^{2}}$

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

$13$

Step 4