Algebra Examples

$(\frac{1}{2}, 0)$ , $(5 \frac{1}{2}, 6)$

Step 1

Convert $5 \frac{1}{2}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$(\frac{1}{2}, 0) - (5 + \frac{1}{2}, 6)$

Step 1.2

Add $5$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{1}{2}, 0) - (5 \cdot \frac{2}{2} + \frac{1}{2}, 6)$

Step 1.2.2

Combine $5$ and $\frac{2}{2}$ .

$(\frac{1}{2}, 0) - (\frac{5 \cdot 2}{2} + \frac{1}{2}, 6)$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{1}{2}, 0) - (\frac{5 \cdot 2 + 1}{2}, 6)$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $5$ by $2$ .

$(\frac{1}{2}, 0) - (\frac{10 + 1}{2}, 6)$

Step 1.2.4.2

Add $10$ and $1$ .

$(\frac{1}{2}, 0) - (\frac{11}{2}, 6)$

Step 2

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 3

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

$\sqrt{{(\frac{11}{2} - \frac{1}{2})}^{2} + {(6 - 0)}^{2}}$

Step 4

Simplify.

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Step 4.1

Combine the numerators over the common denominator.

$\sqrt{{(\frac{11 - 1}{2})}^{2} + {(6 - 0)}^{2}}$

Step 4.2

Simplify the expression.

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Step 4.2.1

Subtract $1$ from $11$ .

$\sqrt{{(\frac{10}{2})}^{2} + {(6 - 0)}^{2}}$

Step 4.2.2

Divide $10$ by $2$ .

$\sqrt{5^{2} + {(6 - 0)}^{2}}$

Step 4.2.3

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

$\sqrt{25 + {(6 - 0)}^{2}}$

Step 4.2.4

Subtract $0$ from $6$ .

$\sqrt{25 + 6^{2}}$

Step 4.2.5

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

$\sqrt{25 + 36}$

Step 4.2.6

Add $25$ and $36$ .

$\sqrt{61}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{61}$

Decimal Form:

$7.81024967 \dots$

Step 6