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

$(5, 1)$ ,

$(11, 1)$

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.

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

Step 3

Simplify.

Subtract

$5$ from

$11$ .

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

Raise

$6$ to the power of

$2$ .

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

Subtract

$1$ from

$1$ .

$\sqrt{36 + 0^{2}}$

Raising

$0$ to any positive power yields

$0$ .

$\sqrt{36 + 0}$

Add

$36$ and

$0$ .

$\sqrt{36}$

Rewrite

$36$ as

$6^{2}$ .

$\sqrt{6^{2}}$

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

$6$

Step 4