Find the Midpoint (1,4) , (9,16)

$(1, 4)$ , $(9, 16)$

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

$(\frac{1 + 9}{2}, \frac{4 + 16}{2})$

Step 3

Add $1$ and $9$ .

$(\frac{10}{2}, \frac{4 + 16}{2})$

Step 4

Divide $10$ by $2$ .

$(5, \frac{4 + 16}{2})$

Step 5

Cancel the common factor of $4 + 16$ and $2$ .

Factor $2$ out of $4$ .

$(5, \frac{2 \cdot 2 + 16}{2})$

Factor $2$ out of $16$ .

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

Factor $2$ out of $2 \cdot 2 + 2 \cdot 8$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 + 8$ by $1$ .

$(5, 2 + 8)$

Step 6

Add $2$ and $8$ .

$(5, 10)$

Step 7