Algebra Examples

$(\frac{π}{4}, 3)$ , $(\frac{π}{2}, 0)$

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.

$\sqrt{{(\frac{π}{2} - \frac{π}{4})}^{2} + {(0 - 3)}^{2}}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

To write $\frac{π}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\sqrt{{(\frac{π}{2} \cdot \frac{2}{2} - \frac{π}{4})}^{2} + {(0 - 3)}^{2}}$

Step 3.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.2.1

Multiply $\frac{π}{2}$ by $\frac{2}{2}$ .

$\sqrt{{(\frac{π \cdot 2}{2 \cdot 2} - \frac{π}{4})}^{2} + {(0 - 3)}^{2}}$

Step 3.2.2

Multiply $2$ by $2$ .

$\sqrt{{(\frac{π \cdot 2}{4} - \frac{π}{4})}^{2} + {(0 - 3)}^{2}}$

Step 3.3

Combine the numerators over the common denominator.

$\sqrt{{(\frac{π \cdot 2 - π}{4})}^{2} + {(0 - 3)}^{2}}$

Step 3.4

Simplify the numerator.

Tap for more steps...

Step 3.4.1

Move $2$ to the left of $π$ .

$\sqrt{{(\frac{2 \cdot π - π}{4})}^{2} + {(0 - 3)}^{2}}$

Step 3.4.2

Subtract $π$ from $2 π$ .

$\sqrt{{(\frac{π}{4})}^{2} + {(0 - 3)}^{2}}$

Step 3.5

Simplify the expression.

Tap for more steps...

Step 3.5.1

Apply the product rule to $\frac{π}{4}$ .

$\sqrt{\frac{π^{2}}{4^{2}} + {(0 - 3)}^{2}}$

Step 3.5.2

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

$\sqrt{\frac{π^{2}}{16} + {(0 - 3)}^{2}}$

Step 3.5.3

Subtract $3$ from $0$ .

$\sqrt{\frac{π^{2}}{16} + {(- 3)}^{2}}$

Step 3.5.4

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

$\sqrt{\frac{π^{2}}{16} + 9}$

Step 3.6

To write $9$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\sqrt{\frac{π^{2}}{16} + 9 \cdot \frac{16}{16}}$

Step 3.7

Combine $9$ and $\frac{16}{16}$ .

$\sqrt{\frac{π^{2}}{16} + \frac{9 \cdot 16}{16}}$

Step 3.8

Simplify the expression.

Tap for more steps...

Step 3.8.1

Combine the numerators over the common denominator.

$\sqrt{\frac{π^{2} + 9 \cdot 16}{16}}$

Step 3.8.2

Multiply $9$ by $16$ .

$\sqrt{\frac{π^{2} + 144}{16}}$

Step 3.9

Rewrite $\sqrt{\frac{π^{2} + 144}{16}}$ as $\frac{\sqrt{π^{2} + 144}}{\sqrt{16}}$ .

$\frac{\sqrt{π^{2} + 144}}{\sqrt{16}}$

Step 3.10

Simplify the denominator.

Tap for more steps...

Step 3.10.1

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{π^{2} + 144}}{\sqrt{4^{2}}}$

Step 3.10.2

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

$\frac{\sqrt{π^{2} + 144}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{π^{2} + 144}}{4}$

Decimal Form:

$3.10110468 \dots$

Step 5