Find the Distance Between Two Points (5,1) , (11,-7)

$(5, 1)$ , $(11, - 7)$

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.

$\sqrt{{(11 - 5)}^{2} + {((- 7) - 1)}^{2}}$

Step 3

Simplify.

Subtract $5$ from $11$ .

$\sqrt{6^{2} + {((- 7) - 1)}^{2}}$

Raise $6$ to the power of $2$ .

$\sqrt{36 + {((- 7) - 1)}^{2}}$

Subtract $1$ from $- 7$ .

$\sqrt{36 + {(- 8)}^{2}}$

Raise $- 8$ to the power of $2$ .

$\sqrt{36 + 64}$

Add $36$ and $64$ .

$\sqrt{100}$

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

$\sqrt{10^{2}}$

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

$10$

Step 4