Find the Distance Between Two Points (5,1) , (5,-6)

$(5, 1)$ , $(5, - 6)$

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.

$\sqrt{{(5 - 5)}^{2} + {((- 6) - 1)}^{2}}$

Step 3

Simplify.

Subtract $5$ from $5$ .

$\sqrt{0^{2} + {((- 6) - 1)}^{2}}$

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

$\sqrt{0 + {((- 6) - 1)}^{2}}$

Subtract $1$ from $- 6$ .

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

Raise $- 7$ to the power of $2$ .

$\sqrt{0 + 49}$

Add $0$ and $49$ .

$\sqrt{49}$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2}}$

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

$7$

Step 4