Find the Midpoint (10,8) , (4,2)

$(10, 8)$ , $(4, 2)$

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

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

Step 3

Cancel the common factor of $10 + 4$ and $2$ .

Factor $2$ out of $10$ .

$(\frac{2 \cdot 5 + 4}{2}, \frac{8 + 2}{2})$

Factor $2$ out of $4$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $5 + 2$ by $1$ .

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

Step 4

Add $5$ and $2$ .

$(7, \frac{8 + 2}{2})$

Step 5

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

Factor $2$ out of $8$ .

$(7, \frac{2 \cdot 4 + 2}{2})$

Factor $2$ out of $2$ .

$(7, \frac{2 \cdot 4 + 2 \cdot 1}{2})$

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

$(7, \frac{2 \cdot (4 + 1)}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(7, \frac{2 \cdot (4 + 1)}{2 (1)})$

Cancel the common factor.

$(7, \frac{2 \cdot (4 + 1)}{2 \cdot 1})$

Rewrite the expression.

$(7, \frac{4 + 1}{1})$

Divide $4 + 1$ by $1$ .

$(7, 4 + 1)$

Step 6

Add $4$ and $1$ .

$(7, 5)$

Step 7

Find the Midpoint (10,8) , (4,2)

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