Find the Midpoint (1/2,-5/2) , (-4/3,-1/6)

$(\frac{1}{2}, - \frac{5}{2})$ , $(- \frac{4}{3}, - \frac{1}{6})$

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

$(\frac{\frac{1}{2} - \frac{4}{3}}{2}, \frac{- \frac{5}{2} - \frac{1}{6}}{2})$

Step 3

Simplify the numerator.

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

$(\frac{\frac{1}{2} \cdot \frac{3}{3} - \frac{4}{3}}{2}, \frac{- \frac{5}{2} - \frac{1}{6}}{2})$

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

$(\frac{\frac{1}{2} \cdot \frac{3}{3} - \frac{4}{3} \cdot \frac{2}{2}}{2}, \frac{- \frac{5}{2} - \frac{1}{6}}{2})$

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

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

$(\frac{\frac{3}{2 \cdot 3} - \frac{4}{3} \cdot \frac{2}{2}}{2}, \frac{- \frac{5}{2} - \frac{1}{6}}{2})$

Multiply $2$ by $3$ .

$(\frac{\frac{3}{6} - \frac{4}{3} \cdot \frac{2}{2}}{2}, \frac{- \frac{5}{2} - \frac{1}{6}}{2})$

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

$(\frac{\frac{3}{6} - \frac{4 \cdot 2}{3 \cdot 2}}{2}, \frac{- \frac{5}{2} - \frac{1}{6}}{2})$

Multiply $3$ by $2$ .

$(\frac{\frac{3}{6} - \frac{4 \cdot 2}{6}}{2}, \frac{- \frac{5}{2} - \frac{1}{6}}{2})$

Combine the numerators over the common denominator.

$(\frac{\frac{3 - 4 \cdot 2}{6}}{2}, \frac{- \frac{5}{2} - \frac{1}{6}}{2})$

Simplify the numerator.

Multiply $- 4$ by $2$ .

$(\frac{\frac{3 - 8}{6}}{2}, \frac{- \frac{5}{2} - \frac{1}{6}}{2})$

Subtract $8$ from $3$ .

$(\frac{\frac{- 5}{6}}{2}, \frac{- \frac{5}{2} - \frac{1}{6}}{2})$

Move the negative in front of the fraction.

$(\frac{- \frac{5}{6}}{2}, \frac{- \frac{5}{2} - \frac{1}{6}}{2})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

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

Step 5

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

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

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

Multiply $2$ by $6$ .

$(- \frac{5}{12}, \frac{- \frac{5}{2} - \frac{1}{6}}{2})$

Step 6

Simplify the numerator.

To write $- \frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(- \frac{5}{12}, \frac{- \frac{5}{2} \cdot \frac{3}{3} - \frac{1}{6}}{2})$

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

Multiply $\frac{5}{2}$ by $\frac{3}{3}$ .

$(- \frac{5}{12}, \frac{- \frac{5 \cdot 3}{2 \cdot 3} - \frac{1}{6}}{2})$

Multiply $2$ by $3$ .

$(- \frac{5}{12}, \frac{- \frac{5 \cdot 3}{6} - \frac{1}{6}}{2})$

Combine the numerators over the common denominator.

$(- \frac{5}{12}, \frac{\frac{- 5 \cdot 3 - 1}{6}}{2})$

Simplify the numerator.

Multiply $- 5$ by $3$ .

$(- \frac{5}{12}, \frac{\frac{- 15 - 1}{6}}{2})$

Subtract $1$ from $- 15$ .

$(- \frac{5}{12}, \frac{\frac{- 16}{6}}{2})$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 16$ and $6$ .

Factor $2$ out of $- 16$ .

$(- \frac{5}{12}, \frac{\frac{2 (- 8)}{6}}{2})$

Cancel the common factors.

Factor $2$ out of $6$ .

$(- \frac{5}{12}, \frac{\frac{2 \cdot - 8}{2 \cdot 3}}{2})$

Cancel the common factor.

$(- \frac{5}{12}, \frac{\frac{2 \cdot - 8}{2 \cdot 3}}{2})$

Rewrite the expression.

$(- \frac{5}{12}, \frac{\frac{- 8}{3}}{2})$

Move the negative in front of the fraction.

$(- \frac{5}{12}, \frac{- \frac{8}{3}}{2})$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$(- \frac{5}{12}, - \frac{8}{3} \cdot \frac{1}{2})$

Step 8

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{8}{3}$ into the numerator.

$(- \frac{5}{12}, \frac{- 8}{3} \cdot \frac{1}{2})$

Factor $2$ out of $- 8$ .

$(- \frac{5}{12}, \frac{2 (- 4)}{3} \cdot \frac{1}{2})$

Cancel the common factor.

$(- \frac{5}{12}, \frac{2 \cdot - 4}{3} \cdot \frac{1}{2})$

Rewrite the expression.

$(- \frac{5}{12}, \frac{- 4}{3})$

Step 9

Move the negative in front of the fraction.

$(- \frac{5}{12}, - \frac{4}{3})$

Step 10

Find the Midpoint (1/2,-5/2) , (-4/3,-1/6)

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