Question

1. point c is on line segment $overline{bd}$. given $bd = 2x$, $cd = 8$, and $bc = x$, determine the numerical length of $overline{bd}$.

Explanation:

Step1: Use segment - addition postulate

Since point C is on line segment $\overline{BD}$, we know that $BD=BC + CD$.
We are given that $BD = 2x$, $CD = 8$, and $BC=x$. So, $2x=x + 8$.

Step2: Solve the equation for x

Subtract x from both sides of the equation $2x=x + 8$.
$2x-x=x + 8-x$, which simplifies to $x = 8$.

Step3: Find the length of BD

We know that $BD = 2x$. Substitute $x = 8$ into the equation for BD.
$BD=2\times8=16$.

Answer:

16