Find the Distance Between Two Points (5,8) , (11,16)

$(5, 8)$ , $(11, 16)$

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.

$\sqrt{{(11 - 5)}^{2} + {(16 - 8)}^{2}}$

Step 3

Simplify.

Subtract $5$ from $11$ .

$\sqrt{6^{2} + {(16 - 8)}^{2}}$

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

$\sqrt{36 + {(16 - 8)}^{2}}$

Subtract $8$ from $16$ .

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

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.

$10$

Step 4