Calculus Examples

$(3, - 54)$ , $(- 3, 54)$

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.

$\sqrt{{((- 3) - 3)}^{2} + {(54 - (- 54))}^{2}}$

Step 3

Simplify.

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Step 3.1

Subtract $3$ from $- 3$ .

$\sqrt{{(- 6)}^{2} + {(54 - (- 54))}^{2}}$

Step 3.2

Raise $- 6$ to the power of $2$ .

$\sqrt{36 + {(54 - (- 54))}^{2}}$

Step 3.3

Multiply $- 1$ by $- 54$ .

$\sqrt{36 + {(54 + 54)}^{2}}$

Step 3.4

Add $54$ and $54$ .

$\sqrt{36 + 108^{2}}$

Step 3.5

Raise $108$ to the power of $2$ .

$\sqrt{36 + 11664}$

Step 3.6

Add $36$ and $11664$ .

$\sqrt{11700}$

Step 3.7

Rewrite $11700$ as $30^{2} \cdot 13$ .

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Step 3.7.1

Factor $900$ out of $11700$ .

$\sqrt{900 (13)}$

Step 3.7.2

Rewrite $900$ as $30^{2}$ .

$\sqrt{30^{2} \cdot 13}$

Step 3.8

Pull terms out from under the radical.

$30 \sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$30 \sqrt{13}$

Decimal Form:

$108.16653826 \dots$

Step 5