Find the Distance Between Two Points (10,2) , (14,5)

$(10, 2)$ , $(14, 5)$

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.

$\sqrt{{(14 - 10)}^{2} + {(5 - 2)}^{2}}$

Step 3

Simplify.

Subtract $10$ from $14$ .

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

Raise $4$ to the power of $2$ .

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

Subtract $2$ from $5$ .

$\sqrt{16 + 3^{2}}$

Raise $3$ to the power of $2$ .

$\sqrt{16 + 9}$

Add $16$ and $9$ .

$\sqrt{25}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2}}$

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

$5$

Step 4