Find the Distance Between Two Points (21,16) , (9,11)

$(21, 16)$ , $(9, 11)$

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.

$\sqrt{{(9 - 21)}^{2} + {(11 - 16)}^{2}}$

Step 3

Simplify.

Subtract $21$ from $9$ .

$\sqrt{{(- 12)}^{2} + {(11 - 16)}^{2}}$

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

$\sqrt{144 + {(11 - 16)}^{2}}$

Subtract $16$ from $11$ .

$\sqrt{144 + {(- 5)}^{2}}$

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