Find the Midpoint (2,2) and (10,8)

$(2, 2)$ and $(10, 8)$

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

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

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $10$ .

$(\frac{2 \cdot 1 + 2 \cdot 5}{2}, \frac{2 + 8}{2})$

Factor $2$ out of $2 \cdot 1 + 2 \cdot 5$ .

$(\frac{2 \cdot (1 + 5)}{2}, \frac{2 + 8}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(\frac{2 \cdot (1 + 5)}{2 (1)}, \frac{2 + 8}{2})$

Cancel the common factor.

$(\frac{2 \cdot (1 + 5)}{2 \cdot 1}, \frac{2 + 8}{2})$

Rewrite the expression.

$(\frac{1 + 5}{1}, \frac{2 + 8}{2})$

Divide $1 + 5$ by $1$ .

$(1 + 5, \frac{2 + 8}{2})$

Add $1$ and $5$ .

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

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

Factor $2$ out of $2$ .

$(6, \frac{2 \cdot 1 + 8}{2})$

Factor $2$ out of $8$ .

$(6, \frac{2 \cdot 1 + 2 \cdot 4}{2})$

Factor $2$ out of $2 \cdot 1 + 2 \cdot 4$ .

$(6, \frac{2 \cdot (1 + 4)}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(6, \frac{2 \cdot (1 + 4)}{2 (1)})$

Cancel the common factor.

$(6, \frac{2 \cdot (1 + 4)}{2 \cdot 1})$

Rewrite the expression.

$(6, \frac{1 + 4}{1})$

Divide $1 + 4$ by $1$ .

$(6, 1 + 4)$

Add $1$ and $4$ .

$(6, 5)$