Algebra Examples

(\frac{7}{8}, - \frac{1}{8})

$(\frac{7}{8}, - \frac{1}{8})$ ,

(- \frac{1}{8}, \frac{7}{8})

$(- \frac{1}{8}, \frac{7}{8})$

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}}

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

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

\sqrt{{((- \frac{1}{8}) - \frac{7}{8})}^{2} + {(\frac{7}{8} - (- \frac{1}{8}))}^{2}}

$\sqrt{{((- \frac{1}{8}) - \frac{7}{8})}^{2} + {(\frac{7}{8} - (- \frac{1}{8}))}^{2}}$

Step 3

Simplify.

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Step 3.1

Combine the numerators over the common denominator.

\sqrt{{(\frac{- 1 - 7}{8})}^{2} + {(\frac{7}{8} - (- \frac{1}{8}))}^{2}}

$\sqrt{{(\frac{- 1 - 7}{8})}^{2} + {(\frac{7}{8} - (- \frac{1}{8}))}^{2}}$

Step 3.2

Simplify the expression.

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Step 3.2.1

Subtract

7

$7$ from

- 1

$- 1$ .

\sqrt{{(\frac{- 8}{8})}^{2} + {(\frac{7}{8} - (- \frac{1}{8}))}^{2}}

$\sqrt{{(\frac{- 8}{8})}^{2} + {(\frac{7}{8} - (- \frac{1}{8}))}^{2}}$

Step 3.2.2

Divide

- 8

$- 8$ by

8

$8$ .

\sqrt{{(- 1)}^{2} + {(\frac{7}{8} - (- \frac{1}{8}))}^{2}}

$\sqrt{{(- 1)}^{2} + {(\frac{7}{8} - (- \frac{1}{8}))}^{2}}$

Step 3.2.3

Raise

- 1

$- 1$ to the power of

2

$2$ .

\sqrt{1 + {(\frac{7}{8} - (- \frac{1}{8}))}^{2}}

$\sqrt{1 + {(\frac{7}{8} - (- \frac{1}{8}))}^{2}}$

\sqrt{1 + {(\frac{7}{8} - (- \frac{1}{8}))}^{2}}

$\sqrt{1 + {(\frac{7}{8} - (- \frac{1}{8}))}^{2}}$

Step 3.3

Multiply

- (- \frac{1}{8})

$- (- \frac{1}{8})$ .

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Step 3.3.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

\sqrt{1 + {(\frac{7}{8} + 1 (\frac{1}{8}))}^{2}}

$\sqrt{1 + {(\frac{7}{8} + 1 (\frac{1}{8}))}^{2}}$

Step 3.3.2

Multiply

\frac{1}{8}

$\frac{1}{8}$ by

1

$1$ .

\sqrt{1 + {(\frac{7}{8} + \frac{1}{8})}^{2}}

$\sqrt{1 + {(\frac{7}{8} + \frac{1}{8})}^{2}}$

\sqrt{1 + {(\frac{7}{8} + \frac{1}{8})}^{2}}

$\sqrt{1 + {(\frac{7}{8} + \frac{1}{8})}^{2}}$

Step 3.4

Combine the numerators over the common denominator.

\sqrt{1 + {(\frac{7 + 1}{8})}^{2}}

$\sqrt{1 + {(\frac{7 + 1}{8})}^{2}}$

Step 3.5

Simplify the expression.

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Step 3.5.1

Add

7

$7$ and

1

$1$ .

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

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

Step 3.5.2

Divide

8

$8$ by

8

$8$ .

\sqrt{1 + 1^{2}}

$\sqrt{1 + 1^{2}}$

Step 3.5.3

One to any power is one.

\sqrt{1 + 1}

$\sqrt{1 + 1}$

Step 3.5.4

Add

1

$1$ and

1

$1$ .

\sqrt{2}

$\sqrt{2}$

\sqrt{2}

$\sqrt{2}$

\sqrt{2}

$\sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\sqrt{2}

$\sqrt{2}$

Decimal Form:

1.41421356 \dots

$1.41421356 \dots$

Step 5