Basic Math Examples

(- \frac{7}{9}, - 3)

$(- \frac{7}{9}, - 3)$ ,

(- \frac{7}{9}, \frac{5}{6})

$(- \frac{7}{9}, \frac{5}{6})$

Step 1

Use the distance formula to determine the distance between the two points.

Distance = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{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{7}{9}) - (- \frac{7}{9}))}^{2} + {(\frac{5}{6} - (- 3))}^{2}}

$\sqrt{{((- \frac{7}{9}) - (- \frac{7}{9}))}^{2} + {(\frac{5}{6} - (- 3))}^{2}}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Multiply

- (- \frac{7}{9})

$- (- \frac{7}{9})$ .

Tap for more steps...

Step 3.1.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

\sqrt{{(- \frac{7}{9} + 1 (\frac{7}{9}))}^{2} + {(\frac{5}{6} - (- 3))}^{2}}

$\sqrt{{(- \frac{7}{9} + 1 (\frac{7}{9}))}^{2} + {(\frac{5}{6} - (- 3))}^{2}}$

Step 3.1.2

Multiply

\frac{7}{9}

$\frac{7}{9}$ by

1

$1$ .

\sqrt{{(- \frac{7}{9} + \frac{7}{9})}^{2} + {(\frac{5}{6} - (- 3))}^{2}}

$\sqrt{{(- \frac{7}{9} + \frac{7}{9})}^{2} + {(\frac{5}{6} - (- 3))}^{2}}$

\sqrt{{(- \frac{7}{9} + \frac{7}{9})}^{2} + {(\frac{5}{6} - (- 3))}^{2}}

$\sqrt{{(- \frac{7}{9} + \frac{7}{9})}^{2} + {(\frac{5}{6} - (- 3))}^{2}}$

Step 3.2

Combine the numerators over the common denominator.

\sqrt{{(\frac{- 7 + 7}{9})}^{2} + {(\frac{5}{6} - (- 3))}^{2}}

$\sqrt{{(\frac{- 7 + 7}{9})}^{2} + {(\frac{5}{6} - (- 3))}^{2}}$

Step 3.3

Simplify the expression.

Tap for more steps...

Step 3.3.1

Add

- 7

$- 7$ and

7

$7$ .

\sqrt{{(\frac{0}{9})}^{2} + {(\frac{5}{6} - (- 3))}^{2}}

$\sqrt{{(\frac{0}{9})}^{2} + {(\frac{5}{6} - (- 3))}^{2}}$

Step 3.3.2

Divide

0

$0$ by

9

$9$ .

\sqrt{0^{2} + {(\frac{5}{6} - (- 3))}^{2}}

$\sqrt{0^{2} + {(\frac{5}{6} - (- 3))}^{2}}$

Step 3.3.3

Raising

0

$0$ to any positive power yields

0

$0$ .

\sqrt{0 + {(\frac{5}{6} - (- 3))}^{2}}

$\sqrt{0 + {(\frac{5}{6} - (- 3))}^{2}}$

Step 3.3.4

Multiply

- 1

$- 1$ by

- 3

$- 3$ .

\sqrt{0 + {(\frac{5}{6} + 3)}^{2}}

$\sqrt{0 + {(\frac{5}{6} + 3)}^{2}}$

\sqrt{0 + {(\frac{5}{6} + 3)}^{2}}

$\sqrt{0 + {(\frac{5}{6} + 3)}^{2}}$

Step 3.4

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{6}{6}

$\frac{6}{6}$ .

\sqrt{0 + {(\frac{5}{6} + 3 \cdot \frac{6}{6})}^{2}}

$\sqrt{0 + {(\frac{5}{6} + 3 \cdot \frac{6}{6})}^{2}}$

Step 3.5

Combine

3

$3$ and

\frac{6}{6}

$\frac{6}{6}$ .

\sqrt{0 + {(\frac{5}{6} + \frac{3 \cdot 6}{6})}^{2}}

$\sqrt{0 + {(\frac{5}{6} + \frac{3 \cdot 6}{6})}^{2}}$

Step 3.6

Combine the numerators over the common denominator.

\sqrt{0 + {(\frac{5 + 3 \cdot 6}{6})}^{2}}

$\sqrt{0 + {(\frac{5 + 3 \cdot 6}{6})}^{2}}$

Step 3.7

Simplify the numerator.

Tap for more steps...

Step 3.7.1

Multiply

3

$3$ by

6

$6$ .

\sqrt{0 + {(\frac{5 + 18}{6})}^{2}}

$\sqrt{0 + {(\frac{5 + 18}{6})}^{2}}$

Step 3.7.2

Add

5

$5$ and

18

$18$ .

\sqrt{0 + {(\frac{23}{6})}^{2}}

$\sqrt{0 + {(\frac{23}{6})}^{2}}$

\sqrt{0 + {(\frac{23}{6})}^{2}}

$\sqrt{0 + {(\frac{23}{6})}^{2}}$

Step 3.8

Apply the product rule to

\frac{23}{6}

$\frac{23}{6}$ .

\sqrt{0 + \frac{23^{2}}{6^{2}}}

$\sqrt{0 + \frac{23^{2}}{6^{2}}}$

Step 3.9

Raise

23

$23$ to the power of

2

$2$ .

\sqrt{0 + \frac{529}{6^{2}}}

$\sqrt{0 + \frac{529}{6^{2}}}$

Step 3.10

Raise

6

$6$ to the power of

2

$2$ .

\sqrt{0 + \frac{529}{36}}

$\sqrt{0 + \frac{529}{36}}$

Step 3.11

Add

0

$0$ and

\frac{529}{36}

$\frac{529}{36}$ .

\sqrt{\frac{529}{36}}

$\sqrt{\frac{529}{36}}$

Step 3.12

Rewrite

$\sqrt{\frac{529}{36}}$ as

$\frac{\sqrt{529}}{\sqrt{36}}$ .

$\frac{\sqrt{529}}{\sqrt{36}}$

Step 3.13

Simplify the numerator.

Tap for more steps...

Step 3.13.1

Rewrite

$529$ as

$23^{2}$ .

$\frac{\sqrt{23^{2}}}{\sqrt{36}}$

Step 3.13.2

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

$\frac{23}{\sqrt{36}}$

Step 3.14

Simplify the denominator.

Tap for more steps...

Step 3.14.1

Rewrite

$36$ as

$6^{2}$ .

$\frac{23}{\sqrt{6^{2}}}$

Step 3.14.2

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

$\frac{23}{6}$

Step 4