Find the Distance Between Two Points (-7/9,-3) , (-7/9,5/6)

$(- \frac{7}{9}, - 3)$ , $(- \frac{7}{9}, \frac{5}{6})$

Step 1

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

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

Step 2

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

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

Step 3

Simplify.

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

Multiply $- 1$ by $- 1$ .

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

Multiply $\frac{7}{9}$ by $1$ .

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Add $- 7$ and $7$ .

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

Divide $0$ by $9$ .

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

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

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

Multiply $- 1$ by $- 3$ .

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

To write $3$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

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

Combine $3$ and $\frac{6}{6}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $6$ .

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

Add $5$ and $18$ .

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

Apply the product rule to $\frac{23}{6}$ .

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

Raise $23$ to the power of $2$ .

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

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

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

Add $0$ and $\frac{529}{36}$ .

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

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

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

Simplify the numerator.

Rewrite $529$ as $23^{2}$ .

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

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

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

Simplify the denominator.

Rewrite $36$ as $6^{2}$ .

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

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

$\frac{23}{6}$

Step 4

Find the Distance Between Two Points (-7/9,-3) , (-7/9,5/6)

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