Find the Midpoint (4,2) and (1,8)

$(4, 2)$ and $(1, 8)$

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

$(\frac{4 + 1}{2}, \frac{2 + 8}{2})$

Step 3

Add $4$ and $1$ .

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

Step 4

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $8$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $1 + 4$ by $1$ .

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

Step 5

Add $1$ and $4$ .

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

Step 6