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

$(5, 2)$ , $(5, - 2)$

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.

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

Step 3

Simplify.

Subtract $5$ from $5$ .

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

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

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

Subtract $2$ from $- 2$ .

$\sqrt{0 + {(- 4)}^{2}}$

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

$\sqrt{0 + 16}$

Add $0$ and $16$ .

$\sqrt{16}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2}}$

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

$4$

Step 4