Precalculus Examples

$(- \frac{8}{3}, \frac{11}{3})$ , $(- \frac{11}{3}, \frac{1}{3})$

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 $(x_{2}, y_{2})$ .

$(\frac{- \frac{8}{3} - \frac{11}{3}}{2}, \frac{\frac{11}{3} + \frac{1}{3}}{2})$

Step 3

Simplify the numerator.

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Step 3.1

Combine the numerators over the common denominator.

$(\frac{\frac{- 8 - 11}{3}}{2}, \frac{\frac{11}{3} + \frac{1}{3}}{2})$

Step 3.2

Subtract $11$ from $- 8$ .

$(\frac{\frac{- 19}{3}}{2}, \frac{\frac{11}{3} + \frac{1}{3}}{2})$

Step 3.3

Move the negative in front of the fraction.

$(\frac{- \frac{19}{3}}{2}, \frac{\frac{11}{3} + \frac{1}{3}}{2})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$(- \frac{19}{3} \cdot \frac{1}{2}, \frac{\frac{11}{3} + \frac{1}{3}}{2})$

Step 5

Multiply $- \frac{19}{3} \cdot \frac{1}{2}$ .

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Step 5.1

Multiply $\frac{1}{2}$ by $\frac{19}{3}$ .

$(- \frac{19}{2 \cdot 3}, \frac{\frac{11}{3} + \frac{1}{3}}{2})$

Step 5.2

Multiply $2$ by $3$ .

$(- \frac{19}{6}, \frac{\frac{11}{3} + \frac{1}{3}}{2})$

Step 6

Simplify the numerator.

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Step 6.1

Combine the numerators over the common denominator.

$(- \frac{19}{6}, \frac{\frac{11 + 1}{3}}{2})$

Step 6.2

Add $11$ and $1$ .

$(- \frac{19}{6}, \frac{\frac{12}{3}}{2})$

Step 6.3

Divide $12$ by $3$ .

$(- \frac{19}{6}, \frac{4}{2})$

Step 7

Divide $4$ by $2$ .

$(- \frac{19}{6}, 2)$

Step 8