Find the Midpoint (8,4) , (10,6)

$(8, 4)$ , $(10, 6)$

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

$(\frac{8 + 10}{2}, \frac{4 + 6}{2})$

Step 3

Cancel the common factor of $8 + 10$ and $2$ .

Factor $2$ out of $8$ .

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

Factor $2$ out of $10$ .

$(\frac{2 \cdot 4 + 2 \cdot 5}{2}, \frac{4 + 6}{2})$

Factor $2$ out of $2 \cdot 4 + 2 \cdot 5$ .

$(\frac{2 \cdot (4 + 5)}{2}, \frac{4 + 6}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(\frac{2 \cdot (4 + 5)}{2 (1)}, \frac{4 + 6}{2})$

Cancel the common factor.

$(\frac{2 \cdot (4 + 5)}{2 \cdot 1}, \frac{4 + 6}{2})$

Rewrite the expression.

$(\frac{4 + 5}{1}, \frac{4 + 6}{2})$

Divide $4 + 5$ by $1$ .

$(4 + 5, \frac{4 + 6}{2})$

Step 4

Add $4$ and $5$ .

$(9, \frac{4 + 6}{2})$

Step 5

Cancel the common factor of $4 + 6$ and $2$ .

Factor $2$ out of $4$ .

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

Factor $2$ out of $6$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 + 3$ by $1$ .

$(9, 2 + 3)$

Step 6

Add $2$ and $3$ .

$(9, 5)$

Step 7

Find the Midpoint (8,4) , (10,6)

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