Precalculus Examples

(12, 12)

$(12, 12)$ ,

(12, 24)

$(12, 24)$

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}}

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

Substitute the actual values of the points into the distance formula.

\sqrt{{(12 - 12)}^{2} + {(24 - 12)}^{2}}

$\sqrt{{(12 - 12)}^{2} + {(24 - 12)}^{2}}$

Step 3

Simplify.

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Step 3.1

Subtract

12

$12$ from

12

$12$ .

\sqrt{0^{2} + {(24 - 12)}^{2}}

$\sqrt{0^{2} + {(24 - 12)}^{2}}$

Step 3.2

Raising

0

$0$ to any positive power yields

0

$0$ .

\sqrt{0 + {(24 - 12)}^{2}}

$\sqrt{0 + {(24 - 12)}^{2}}$

Step 3.3

Subtract

12

$12$ from

24

$24$ .

\sqrt{0 + 12^{2}}

$\sqrt{0 + 12^{2}}$

Step 3.4

Raise

12

$12$ to the power of

2

$2$ .

\sqrt{0 + 144}

$\sqrt{0 + 144}$

Step 3.5

Add

0

$0$ and

144

$144$ .

\sqrt{144}

$\sqrt{144}$

Step 3.6

Rewrite

144

$144$ as

12^{2}

$12^{2}$ .

\sqrt{12^{2}}

$\sqrt{12^{2}}$

Step 3.7

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

12

$12$

12

$12$

Step 4

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