Find the Distance Between Two Points (5,3) , (13,9)

$(5, 3)$ , $(13, 9)$

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.

$\sqrt{{(13 - 5)}^{2} + {(9 - 3)}^{2}}$

Step 3

Simplify.

Subtract $5$ from $13$ .

$\sqrt{8^{2} + {(9 - 3)}^{2}}$

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

$\sqrt{64 + {(9 - 3)}^{2}}$

Subtract $3$ from $9$ .

$\sqrt{64 + 6^{2}}$

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

$\sqrt{64 + 36}$

Add $64$ and $36$ .

$\sqrt{100}$

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

$\sqrt{10^{2}}$

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

$10$

Step 4