Find the Midpoint P_1=(2,-3) , P_2=(4,5)

$P_{1} = (2, - 3)$ , $P_{2} = (4, 5)$

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

$(\frac{2 + 4}{2}, \frac{- 3 + 5}{2})$

Step 3

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

Factor $2$ out of $2$ .

$(\frac{2 \cdot 1 + 4}{2}, \frac{- 3 + 5}{2})$

Factor $2$ out of $4$ .

$(\frac{2 \cdot 1 + 2 \cdot 2}{2}, \frac{- 3 + 5}{2})$

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

$(\frac{2 \cdot (1 + 2)}{2}, \frac{- 3 + 5}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(\frac{2 \cdot (1 + 2)}{2 (1)}, \frac{- 3 + 5}{2})$

Cancel the common factor.

$(\frac{2 \cdot (1 + 2)}{2 \cdot 1}, \frac{- 3 + 5}{2})$

Rewrite the expression.

$(\frac{1 + 2}{1}, \frac{- 3 + 5}{2})$

Divide $1 + 2$ by $1$ .

$(1 + 2, \frac{- 3 + 5}{2})$

Step 4

Add $1$ and $2$ .

$(3, \frac{- 3 + 5}{2})$

Step 5

Add $- 3$ and $5$ .

$(3, \frac{2}{2})$

Step 6

Divide $2$ by $2$ .

$(3, 1)$

Step 7