Algebra Examples

$(- \frac{3}{8}, 3)$ , $(- \frac{3}{8}, \frac{1}{2})$

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.

$\sqrt{{((- \frac{3}{8}) - (- \frac{3}{8}))}^{2} + {(\frac{1}{2} - 3)}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- (- \frac{3}{8})$ .

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Step 3.1.1

Multiply $- 1$ by $- 1$ .

$\sqrt{{(- \frac{3}{8} + 1 (\frac{3}{8}))}^{2} + {(\frac{1}{2} - 3)}^{2}}$

Step 3.1.2

Multiply $\frac{3}{8}$ by $1$ .

$\sqrt{{(- \frac{3}{8} + \frac{3}{8})}^{2} + {(\frac{1}{2} - 3)}^{2}}$

Step 3.2

Combine the numerators over the common denominator.

$\sqrt{{(\frac{- 3 + 3}{8})}^{2} + {(\frac{1}{2} - 3)}^{2}}$

Step 3.3

Simplify the expression.

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Step 3.3.1

Add $- 3$ and $3$ .

$\sqrt{{(\frac{0}{8})}^{2} + {(\frac{1}{2} - 3)}^{2}}$

Step 3.3.2

Divide $0$ by $8$ .

$\sqrt{0^{2} + {(\frac{1}{2} - 3)}^{2}}$

Step 3.3.3

Raising $0$ to any positive power yields $0$ .

$\sqrt{0 + {(\frac{1}{2} - 3)}^{2}}$

Step 3.4

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\sqrt{0 + {(\frac{1}{2} - 3 \cdot \frac{2}{2})}^{2}}$

Step 3.5

Combine $- 3$ and $\frac{2}{2}$ .

$\sqrt{0 + {(\frac{1}{2} + \frac{- 3 \cdot 2}{2})}^{2}}$

Step 3.6

Combine the numerators over the common denominator.

$\sqrt{0 + {(\frac{1 - 3 \cdot 2}{2})}^{2}}$

Step 3.7

Simplify the numerator.

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Step 3.7.1

Multiply $- 3$ by $2$ .

$\sqrt{0 + {(\frac{1 - 6}{2})}^{2}}$

Step 3.7.2

Subtract $6$ from $1$ .

$\sqrt{0 + {(\frac{- 5}{2})}^{2}}$

Step 3.8

Move the negative in front of the fraction.

$\sqrt{0 + {(- \frac{5}{2})}^{2}}$

Step 3.9

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.9.1

Apply the product rule to $- \frac{5}{2}$ .

$\sqrt{0 + {(- 1)}^{2} {(\frac{5}{2})}^{2}}$

Step 3.9.2

Apply the product rule to $\frac{5}{2}$ .

$\sqrt{0 + {(- 1)}^{2} \frac{5^{2}}{2^{2}}}$

Step 3.10

Raise $- 1$ to the power of $2$ .

$\sqrt{0 + 1 \frac{5^{2}}{2^{2}}}$

Step 3.11

Multiply $\frac{5^{2}}{2^{2}}$ by $1$ .

$\sqrt{0 + \frac{5^{2}}{2^{2}}}$

Step 3.12

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

$\sqrt{0 + \frac{25}{2^{2}}}$

Step 3.13

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

$\sqrt{0 + \frac{25}{4}}$

Step 3.14

Add $0$ and $\frac{25}{4}$ .

$\sqrt{\frac{25}{4}}$

Step 3.15

Rewrite $\sqrt{\frac{25}{4}}$ as $\frac{\sqrt{25}}{\sqrt{4}}$ .

$\frac{\sqrt{25}}{\sqrt{4}}$

Step 3.16

Simplify the numerator.

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Step 3.16.1

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

$\frac{\sqrt{5^{2}}}{\sqrt{4}}$

Step 3.16.2

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

$\frac{5}{\sqrt{4}}$

Step 3.17

Simplify the denominator.

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Step 3.17.1

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

$\frac{5}{\sqrt{2^{2}}}$

Step 3.17.2

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

$\frac{5}{2}$

Step 4