Algebra Examples

$(- \frac{1}{9}, - \frac{1}{2})$ , $(\frac{14}{9}, \frac{4}{3})$

Step 1

Use the midpoint formula to find the midpoint of the line segment.

$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Step 2

Substitute in the values for $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

$(\frac{- \frac{1}{9} + \frac{14}{9}}{2}, \frac{- \frac{1}{2} + \frac{4}{3}}{2})$

Step 3

Simplify the numerator.

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Step 3.1

Combine the numerators over the common denominator.

$(\frac{\frac{- 1 + 14}{9}}{2}, \frac{- \frac{1}{2} + \frac{4}{3}}{2})$

Step 3.2

Add $- 1$ and $14$ .

$(\frac{\frac{13}{9}}{2}, \frac{- \frac{1}{2} + \frac{4}{3}}{2})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$(\frac{13}{9} \cdot \frac{1}{2}, \frac{- \frac{1}{2} + \frac{4}{3}}{2})$

Step 5

Multiply $\frac{13}{9} \cdot \frac{1}{2}$ .

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Step 5.1

Multiply $\frac{13}{9}$ by $\frac{1}{2}$ .

$(\frac{13}{9 \cdot 2}, \frac{- \frac{1}{2} + \frac{4}{3}}{2})$

Step 5.2

Multiply $9$ by $2$ .

$(\frac{13}{18}, \frac{- \frac{1}{2} + \frac{4}{3}}{2})$

Step 6

Simplify the numerator.

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Step 6.1

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{13}{18}, \frac{- \frac{1}{2} \cdot \frac{3}{3} + \frac{4}{3}}{2})$

Step 6.2

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{13}{18}, \frac{- \frac{1}{2} \cdot \frac{3}{3} + \frac{4}{3} \cdot \frac{2}{2}}{2})$

Step 6.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.3.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$(\frac{13}{18}, \frac{- \frac{3}{2 \cdot 3} + \frac{4}{3} \cdot \frac{2}{2}}{2})$

Step 6.3.2

Multiply $2$ by $3$ .

$(\frac{13}{18}, \frac{- \frac{3}{6} + \frac{4}{3} \cdot \frac{2}{2}}{2})$

Step 6.3.3

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

$(\frac{13}{18}, \frac{- \frac{3}{6} + \frac{4 \cdot 2}{3 \cdot 2}}{2})$

Step 6.3.4

Multiply $3$ by $2$ .

$(\frac{13}{18}, \frac{- \frac{3}{6} + \frac{4 \cdot 2}{6}}{2})$

Step 6.4

Combine the numerators over the common denominator.

$(\frac{13}{18}, \frac{\frac{- 3 + 4 \cdot 2}{6}}{2})$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply $4$ by $2$ .

$(\frac{13}{18}, \frac{\frac{- 3 + 8}{6}}{2})$

Step 6.5.2

Add $- 3$ and $8$ .

$(\frac{13}{18}, \frac{\frac{5}{6}}{2})$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$(\frac{13}{18}, \frac{5}{6} \cdot \frac{1}{2})$

Step 8

Multiply $\frac{5}{6} \cdot \frac{1}{2}$ .

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Step 8.1

Multiply $\frac{5}{6}$ by $\frac{1}{2}$ .

$(\frac{13}{18}, \frac{5}{6 \cdot 2})$

Step 8.2

Multiply $6$ by $2$ .

$(\frac{13}{18}, \frac{5}{12})$

Step 9