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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Multiply $- 1$ by $1$ to get $- 1$ .

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

Subtract $1$ from $3$ to get $2$ .

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

Remove parentheses around $2$ .

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

Raise $2$ to the power of $2$ to get $4$ .

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

Multiply $- 1$ by $1$ to get $- 1$ .

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

Subtract $1$ from $3$ to get $2$ .

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

Remove parentheses around $2$ .

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

Raise $2$ to the power of $2$ to get $4$ .

$\sqrt{4 + 4}$

Add $4$ and $4$ to get $8$ .

$\sqrt{8}$

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 approximate value for the distance between the two points is $2.82842712$ .

$2 \sqrt{2} \approx 2.82842712$

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