Precalculus Examples

$(1, 1)$ , $(3, 3)$

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.

$\sqrt{{(3 - 1)}^{2} + {(3 - 1)}^{2}}$

Simplify.

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Subtract $1$ from $3$ .

$\sqrt{2^{2} + {(3 - 1)}^{2}}$

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

$\sqrt{4 + {(3 - 1)}^{2}}$

Subtract $1$ from $3$ .

$\sqrt{4 + 2^{2}}$

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

$\sqrt{4 + 4}$

Add $4$ and $4$ .

$\sqrt{8}$

Rewrite $8$ as $2^{2} \cdot 2$ .

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Factor $4$ out of $8$ .

$\sqrt{4 (2)}$

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

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

Pull terms out from under the radical.

$2 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$

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