Find the Midpoint (8,1) , (10,7)

$(8, 1)$ , $(10, 7)$

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

$(\frac{8 + 10}{2}, \frac{1 + 7}{2})$

Cancel the common factor of $8 + 10$ and $2$ .

Factor $2$ out of $8$ .

$(\frac{2 \cdot 4 + 10}{2}, \frac{1 + 7}{2})$

Factor $2$ out of $10$ .

$(\frac{2 \cdot 4 + 2 \cdot 5}{2}, \frac{1 + 7}{2})$

Factor $2$ out of $2 \cdot 4 + 2 \cdot 5$ .

$(\frac{2 \cdot (4 + 5)}{2}, \frac{1 + 7}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(\frac{2 \cdot (4 + 5)}{2 (1)}, \frac{1 + 7}{2})$

Cancel the common factor.

$(\frac{2 \cdot (4 + 5)}{2 \cdot 1}, \frac{1 + 7}{2})$

Rewrite the expression.

$(\frac{4 + 5}{1}, \frac{1 + 7}{2})$

Divide $4 + 5$ by $1$ .

$(4 + 5, \frac{1 + 7}{2})$

Add $4$ and $5$ .

$(9, \frac{1 + 7}{2})$

Add $1$ and $7$ .

$(9, \frac{8}{2})$

Divide $8$ by $2$ .

$(9, 4)$