Find the Midpoint P_1=(2,-6) , P_2=(4,6)

$P_{1} = (2, - 6)$ , $P_{2} = (4, 6)$

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

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

Step 3

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $4$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $1 + 2$ by $1$ .

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

Step 4

Add $1$ and $2$ .

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

Step 5

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

Factor $2$ out of $- 6$ .

$(3, \frac{2 \cdot - 3 + 6}{2})$

Factor $2$ out of $6$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$(3, \frac{- 3 + 3}{1})$

Divide $- 3 + 3$ by $1$ .

$(3, - 3 + 3)$

Step 6

Add $- 3$ and $3$ .

$(3, 0)$

Step 7

Find the Midpoint P_1=(2,-6) , P_2=(4,6)

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