Precalculus Examples

$(12, 12)$ , $(12, 129)$

Use the distance formula to determine the distance between the two points.

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

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

$\sqrt{{(12 - 12)}^{2} + {(129 - 12)}^{2}}$

Simplify.

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Subtract $12$ from $12$ .

$\sqrt{{(0)}^{2} + {(129 - 12)}^{2}}$

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

$\sqrt{0 + {(129 - 12)}^{2}}$

Subtract $12$ from $129$ .

$\sqrt{0 + {(117)}^{2}}$

Raise $117$ to the power of $2$ .

$\sqrt{0 + 13689}$

Add $0$ and $13689$ .

$\sqrt{13689}$

Rewrite $13689$ as $117^{2}$ .

$\sqrt{117^{2}}$

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

$117$

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