Find the Midpoint (8,2) , (6,10)

$(8, 2)$ , $(6, 10)$

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

$(\frac{8 + 6}{2}, \frac{2 + 10}{2})$

Step 3

Cancel the common factor of $8 + 6$ and $2$ .

Factor $2$ out of $8$ .

$(\frac{2 \cdot 4 + 6}{2}, \frac{2 + 10}{2})$

Factor $2$ out of $6$ .

$(\frac{2 \cdot 4 + 2 \cdot 3}{2}, \frac{2 + 10}{2})$

Factor $2$ out of $2 \cdot 4 + 2 \cdot 3$ .

$(\frac{2 \cdot (4 + 3)}{2}, \frac{2 + 10}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(\frac{2 \cdot (4 + 3)}{2 (1)}, \frac{2 + 10}{2})$

Cancel the common factor.

$(\frac{2 \cdot (4 + 3)}{2 \cdot 1}, \frac{2 + 10}{2})$

Rewrite the expression.

$(\frac{4 + 3}{1}, \frac{2 + 10}{2})$

Divide $4 + 3$ by $1$ .

$(4 + 3, \frac{2 + 10}{2})$

Step 4

Add $4$ and $3$ .

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

Step 5

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $10$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $1 + 5$ by $1$ .

$(7, 1 + 5)$

Step 6

Add $1$ and $5$ .

$(7, 6)$

Step 7

Find the Midpoint (8,2) , (6,10)

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