Question

1. if b is the mid - point of $overline{ac}$, and $ac = 8x - 20$, find bc.

a
$3x - 1$
b
c

Explanation:

Step1: Use mid - point property

Since B is the mid - point of $\overline{AC}$, then $AB = BC$ and $AC=AB + BC = 2AB=2BC$. So, $AB=\frac{1}{2}AC$. Given $AB = 3x - 1$ and $AC = 8x-20$, we have $3x - 1=\frac{1}{2}(8x - 20)$.

Step2: Solve the equation for x

First, expand the right - hand side: $3x - 1 = 4x-10$. Then, move the x terms to one side: $4x-3x=10 - 1$. So, $x = 9$.

Step3: Find the length of BC

Since $BC = AB = 3x - 1$, substitute $x = 9$ into the expression for $BC$. Then $BC=3\times9 - 1=27 - 1=26$.

Answer:

$26$