Find the Midpoint (10,5) and (6,9)

$(10, 5)$ and $(6, 9)$

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

$(\frac{10 + 6}{2}, \frac{5 + 9}{2})$

Step 3

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

Factor $2$ out of $10$ .

$(\frac{2 \cdot 5 + 6}{2}, \frac{5 + 9}{2})$

Factor $2$ out of $6$ .

$(\frac{2 \cdot 5 + 2 \cdot 3}{2}, \frac{5 + 9}{2})$

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

$(\frac{2 \cdot (5 + 3)}{2}, \frac{5 + 9}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(\frac{2 \cdot (5 + 3)}{2 (1)}, \frac{5 + 9}{2})$

Cancel the common factor.

$(\frac{2 \cdot (5 + 3)}{2 \cdot 1}, \frac{5 + 9}{2})$

Rewrite the expression.

$(\frac{5 + 3}{1}, \frac{5 + 9}{2})$

Divide $5 + 3$ by $1$ .

$(5 + 3, \frac{5 + 9}{2})$

Step 4

Add $5$ and $3$ .

$(8, \frac{5 + 9}{2})$

Step 5

Add $5$ and $9$ .

$(8, \frac{14}{2})$

Step 6

Divide $14$ by $2$ .

$(8, 7)$

Step 7