Question

B is the midpoint of AC . AB=6x-2 and BC=2x+10.Find the value of x and the length of the segment indicatedx=AC=

Answer 1

Answer:

x=3 units

AC=32 units

Explanation:

If B is the midpoint of AC, it means B divides line AC into two equal parts AB and BC.

$\begin{gathered} AB=BC \\ 6x-2=2x+10 \\ 6x-2x=10+2 \\ 4x=12 \\ \frac{4x}{4}=\frac{12}{4} \\ x=3 \end{gathered}$

Next, we find the value of AC.

$\begin{gathered} AB=6x-2 \\ =6(3)-2 \\ =18-2 \\ =16 \\ \text{Therefore:} \\ AC=AB\times2 \\ =16\times2 \\ =32 \end{gathered}$