Find the Distance Between Two Points (5,3) , (5,-7)

$(5, 3)$ , $(5, - 7)$

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.

$\sqrt{{(5 - 5)}^{2} + {((- 7) - 3)}^{2}}$

Step 3

Simplify.

Subtract $5$ from $5$ .

$\sqrt{0^{2} + {((- 7) - 3)}^{2}}$

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

$\sqrt{0 + {((- 7) - 3)}^{2}}$

Subtract $3$ from $- 7$ .

$\sqrt{0 + {(- 10)}^{2}}$

Raise $- 10$ to the power of $2$ .

$\sqrt{0 + 100}$

Add $0$ and $100$ .

$\sqrt{100}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2}}$

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

$10$

Step 4