Find the Midpoint (1/3,7/2) , (4/3,3/2)

$(\frac{1}{3}, \frac{7}{2})$ , $(\frac{4}{3}, \frac{3}{2})$

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

$(\frac{\frac{1}{3} + \frac{4}{3}}{2}, \frac{\frac{7}{2} + \frac{3}{2}}{2})$

Step 3

Simplify the numerator.

Combine the numerators over the common denominator.

$(\frac{\frac{1 + 4}{3}}{2}, \frac{\frac{7}{2} + \frac{3}{2}}{2})$

Add $1$ and $4$ .

$(\frac{\frac{5}{3}}{2}, \frac{\frac{7}{2} + \frac{3}{2}}{2})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$(\frac{5}{3} \cdot \frac{1}{2}, \frac{\frac{7}{2} + \frac{3}{2}}{2})$

Step 5

Multiply $\frac{5}{3} \cdot \frac{1}{2}$ .

Multiply $\frac{5}{3}$ by $\frac{1}{2}$ .

$(\frac{5}{3 \cdot 2}, \frac{\frac{7}{2} + \frac{3}{2}}{2})$

Multiply $3$ by $2$ .

$(\frac{5}{6}, \frac{\frac{7}{2} + \frac{3}{2}}{2})$

Step 6

Simplify the numerator.

Combine the numerators over the common denominator.

$(\frac{5}{6}, \frac{\frac{7 + 3}{2}}{2})$

Add $7$ and $3$ .

$(\frac{5}{6}, \frac{\frac{10}{2}}{2})$

Divide $10$ by $2$ .

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

Step 7