Find the Distance Between Two Points What is the distance between the points (-2,5) and (2,8) ?

What is the distance between the points $(- 2, 5)$ and $(2, 8)$ ?

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Substitute the actual values of the points into the distance formula.

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

Simplify.

Multiply $- 1$ by $- 2$ .

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

Add $2$ and $2$ .

$\sqrt{4^{2} + {(8 - 5)}^{2}}$

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

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

Subtract $5$ from $8$ .

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

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.

$5$