Precalculus Examples

$(67, 95)$ , $(- 9, - 3)$

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.

$\sqrt{{((- 9) - (67))}^{2} + {((- 3) - (95))}^{2}}$

Simplify.

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Multiply $- 1$ by $67$ .

$\sqrt{{(- 9 - 67)}^{2} + {((- 3) - (95))}^{2}}$

Subtract $67$ from $- 9$ .

$\sqrt{{(- 76)}^{2} + {((- 3) - (95))}^{2}}$

Raise $- 76$ to the power of $2$ .

$\sqrt{5776 + {((- 3) - (95))}^{2}}$

Multiply $- 1$ by $95$ .

$\sqrt{5776 + {(- 3 - 95)}^{2}}$

Subtract $95$ from $- 3$ .

$\sqrt{5776 + {(- 98)}^{2}}$

Raise $- 98$ to the power of $2$ .

$\sqrt{5776 + 9604}$

Add $5776$ and $9604$ .

$\sqrt{15380}$

Rewrite $15380$ as $2^{2} \cdot 3845$ .

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Factor $4$ out of $15380$ .

$\sqrt{4 (3845)}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 3845}$

Pull terms out from under the radical.

$2 \sqrt{3845}$

The approximate value for the distance between the two points is $124.01612798$ .

$2 \sqrt{3845} \approx 124.01612798$

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