Precalculus Examples

$(5, 12)$ , $(35, 17)$

Step 1

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

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

Step 2

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

$\sqrt{{(35 - 5)}^{2} + {(17 - 12)}^{2}}$

Step 3

Simplify.

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Step 3.1

Subtract $5$ from $35$ .

$\sqrt{30^{2} + {(17 - 12)}^{2}}$

Step 3.2

Raise $30$ to the power of $2$ .

$\sqrt{900 + {(17 - 12)}^{2}}$

Step 3.3

Subtract $12$ from $17$ .

$\sqrt{900 + 5^{2}}$

Step 3.4

Raise $5$ to the power of $2$ .

$\sqrt{900 + 25}$

Step 3.5

Add $900$ and $25$ .

$\sqrt{925}$

Step 3.6

Rewrite $925$ as $5^{2} \cdot 37$ .

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Step 3.6.1

Factor $25$ out of $925$ .

$\sqrt{25 (37)}$

Step 3.6.2

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 37}$

Step 3.7

Pull terms out from under the radical.

$5 \sqrt{37}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{37}$

Decimal Form:

$30.41381265 \dots$

Step 5