Precalculus Examples

$(3, \frac{11 π}{12})$ , $(1, \frac{5 π}{4})$

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.

$\sqrt{{(1 - 3)}^{2} + {(\frac{5 π}{4} - \frac{11 π}{12})}^{2}}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Subtract $3$ from $1$ .

$\sqrt{{(- 2)}^{2} + {(\frac{5 π}{4} - \frac{11 π}{12})}^{2}}$

Step 3.2

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

$\sqrt{4 + {(\frac{5 π}{4} - \frac{11 π}{12})}^{2}}$

Step 3.3

To write $\frac{5 π}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\sqrt{4 + {(\frac{5 π}{4} \cdot \frac{3}{3} - \frac{11 π}{12})}^{2}}$

Step 3.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.4.1

Multiply $\frac{5 π}{4}$ by $\frac{3}{3}$ .

$\sqrt{4 + {(\frac{5 π \cdot 3}{4 \cdot 3} - \frac{11 π}{12})}^{2}}$

Step 3.4.2

Multiply $4$ by $3$ .

$\sqrt{4 + {(\frac{5 π \cdot 3}{12} - \frac{11 π}{12})}^{2}}$

Step 3.5

Combine the numerators over the common denominator.

$\sqrt{4 + {(\frac{5 π \cdot 3 - 11 π}{12})}^{2}}$

Step 3.6

Simplify the numerator.

Tap for more steps...

Step 3.6.1

Multiply $3$ by $5$ .

$\sqrt{4 + {(\frac{15 π - 11 π}{12})}^{2}}$

Step 3.6.2

Subtract $11 π$ from $15 π$ .

$\sqrt{4 + {(\frac{4 π}{12})}^{2}}$

Step 3.7

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.7.1

Cancel the common factor of $4$ and $12$ .

Tap for more steps...

Step 3.7.1.1

Factor $4$ out of $4 π$ .

$\sqrt{4 + {(\frac{4 (π)}{12})}^{2}}$

Step 3.7.1.2

Cancel the common factors.

Tap for more steps...

Step 3.7.1.2.1

Factor $4$ out of $12$ .

$\sqrt{4 + {(\frac{4 π}{4 \cdot 3})}^{2}}$

Step 3.7.1.2.2

Cancel the common factor.

$\sqrt{4 + {(\frac{4 π}{4 \cdot 3})}^{2}}$

Step 3.7.1.2.3

Rewrite the expression.

$\sqrt{4 + {(\frac{π}{3})}^{2}}$

Step 3.7.2

Simplify the expression.

Tap for more steps...

Step 3.7.2.1

Apply the product rule to $\frac{π}{3}$ .

$\sqrt{4 + \frac{π^{2}}{3^{2}}}$

Step 3.7.2.2

Raise $3$ to the power of $2$ .

$\sqrt{4 + \frac{π^{2}}{9}}$

Step 3.8

To write $4$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\sqrt{4 \cdot \frac{9}{9} + \frac{π^{2}}{9}}$

Step 3.9

Combine $4$ and $\frac{9}{9}$ .

$\sqrt{\frac{4 \cdot 9}{9} + \frac{π^{2}}{9}}$

Step 3.10

Simplify the expression.

Tap for more steps...

Step 3.10.1

Combine the numerators over the common denominator.

$\sqrt{\frac{4 \cdot 9 + π^{2}}{9}}$

Step 3.10.2

Multiply $4$ by $9$ .

$\sqrt{\frac{36 + π^{2}}{9}}$

Step 3.11

Rewrite $\sqrt{\frac{36 + π^{2}}{9}}$ as $\frac{\sqrt{36 + π^{2}}}{\sqrt{9}}$ .

$\frac{\sqrt{36 + π^{2}}}{\sqrt{9}}$

Step 3.12

Simplify the denominator.

Tap for more steps...

Step 3.12.1

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{36 + π^{2}}}{\sqrt{3^{2}}}$

Step 3.12.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{\sqrt{36 + π^{2}}}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{36 + π^{2}}}{3}$

Decimal Form:

$2.25757008 \dots$

Step 5