Question

the midpoint of $overline{bd}$ is

given: parallelogram $abcd$
prove: $overline{ac}$ bisects $overline{bd}$, and $overline{bd}$ bisects $overline{ac}$.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Identify coordinates of B and D

For point $B(2b,2c)$ and point $D(2a,0)$, where $x_1 = 2b,y_1=2c,x_2 = 2a,y_2 = 0$.

Step3: Calculate the mid - point

Substitute the values into the mid - point formula: $\frac{2b+2a}{2}=\ a + b$ and $\frac{2c + 0}{2}=c$. So the mid - point is $(a + b,c)$.

Answer:

$(a + b,c)$