Find the Distance Between Two Points (-3,5) and (-3,2)

$(- 3, 5)$ and $(- 3, 2)$

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.

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

Simplify.

Multiply $- 1$ by $- 3$ .

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

Add $- 3$ and $3$ .

$\sqrt{0^{2} + {(2 - 5)}^{2}}$

Raising $0$ to any positive power yields $0$ .

$\sqrt{0 + {(2 - 5)}^{2}}$

Subtract $5$ from $2$ .

$\sqrt{0 + {(- 3)}^{2}}$

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

$\sqrt{0 + 9}$

Add $0$ and $9$ .

$\sqrt{9}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2}}$

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

$3$