Find the Distance Between Two Points (3,-7) and (3,8)

$(3, - 7)$ and $(3, 8)$

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.

$\sqrt{{(3 - 3)}^{2} + {(8 - (- 7))}^{2}}$

Simplify.

Subtract $3$ from $3$ .

$\sqrt{0^{2} + {(8 - (- 7))}^{2}}$

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

$\sqrt{0 + {(8 - (- 7))}^{2}}$

Multiply $- 1$ by $- 7$ .

$\sqrt{0 + {(8 + 7)}^{2}}$

Add $8$ and $7$ .

$\sqrt{0 + 15^{2}}$

Raise $15$ to the power of $2$ .

$\sqrt{0 + 225}$

Add $0$ and $225$ .

$\sqrt{225}$

Rewrite $225$ as $15^{2}$ .

$\sqrt{15^{2}}$

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

$15$