jaycee is writing a coordinate proof to show that the diagonals of a rectangle bisect each other. she starts by assigning coordinates to a rectangle. then she uses these coordinates to write the coordinates of the midpoint of each diagonal. she finds that the midpoints of the diagonals have the same coordinates, so the diagonals must bisect each other. what are the coordinates of the midpoint of the diagonals of the rectangle? enter expressions in the box for the coordinates of the midpoint.

Question

Accepted Answer

# Explanation:
## Step1: Find midpoint of diagonal $ DF $
The midpoint formula is $ (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2}) $. For points $ D(0,b) $ and $ F(a,0) $, $ x_1 = 0,y_1 = b,x_2 = a,y_2 = 0 $.
$$
\begin{align*}
x&=\frac{0 + a}{2}=\frac{a}{2}\
y&=\frac{b+0}{2}=\frac{b}{2}
\end{align*}
$$
## Step2: Find midpoint of diagonal $ GE $
For points $ G(0,0) $ and $ E(a,b) $, $ x_1 = 0,y_1 = 0,x_2 = a,y_2 = b $.
$$
\begin{align*}
x&=\frac{0 + a}{2}=\frac{a}{2}\
y&=\frac{0 + b}{2}=\frac{b}{2}
\end{align*}
$$

# Answer:
$(\frac{a}{2},\frac{b}{2})$

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Question

Explanation:

Step1: Find midpoint of diagonal \( DF \)

Step2: Find midpoint of diagonal \( GE \)

Answer: