Find the Distance Between Two Points (4,5) , (10,13)

$(4, 5)$ , $(10, 13)$

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.

$\sqrt{{(10 - 4)}^{2} + {(13 - 5)}^{2}}$

Step 3

Simplify.

Subtract $4$ from $10$ .

$\sqrt{6^{2} + {(13 - 5)}^{2}}$

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

$\sqrt{36 + {(13 - 5)}^{2}}$

Subtract $5$ from $13$ .

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

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