Find the Midpoint (10,7) and (2,1)

$(10, 7)$ and $(2, 1)$

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

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

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

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

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

Factor $2$ out of $10$ .

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

Factor $2$ out of $2$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $5 + 1$ by $1$ .

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

Add $5$ and $1$ .

$(6, \frac{7 + 1}{2})$

Add $7$ and $1$ .

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

Divide $8$ by $2$ .

$(6, 4)$