Find the Midpoint (2,1) , (4,5)

$(2, 1)$ , $(4, 5)$

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

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

Step 3

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $4$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $1 + 2$ by $1$ .

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

Step 4

Add $1$ and $2$ .

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

Step 5

Add $1$ and $5$ .

$(3, \frac{6}{2})$

Step 6

Divide $6$ by $2$ .

$(3, 3)$

Step 7