Find the Midpoint (3,10) and (8,6)

$(3, 10)$ and $(8, 6)$

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

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

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

$(\frac{3 + 8}{2}, \frac{10 + 6}{2})$

Add $3$ and $8$ .

$(\frac{11}{2}, \frac{10 + 6}{2})$

Cancel the common factor of $10 + 6$ and $2$ .

Factor $2$ out of $10$ .

$(\frac{11}{2}, \frac{2 \cdot 5 + 6}{2})$

Factor $2$ out of $6$ .

$(\frac{11}{2}, \frac{2 \cdot 5 + 2 \cdot 3}{2})$

Factor $2$ out of $2 \cdot 5 + 2 \cdot 3$ .

$(\frac{11}{2}, \frac{2 \cdot (5 + 3)}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(\frac{11}{2}, \frac{2 \cdot (5 + 3)}{2 (1)})$

Cancel the common factor.

$(\frac{11}{2}, \frac{2 \cdot (5 + 3)}{2 \cdot 1})$

Rewrite the expression.

$(\frac{11}{2}, \frac{5 + 3}{1})$

Divide $5 + 3$ by $1$ .

$(\frac{11}{2}, 5 + 3)$

Add $5$ and $3$ .

$(\frac{11}{2}, 8)$