Question

Point B is the midpoint (or bisector) of line segment AC. Given that BC = 15x and AB = 8x + 28, what is the length of segment AC?

Answer 1

Since the point "B" is the bisector of the line, it means that it divides the line in two equal parts, so the length of the whole segment is the sum of each part.

`AC\text{ = AB+BC}`

To find that length we first need to find the value of "x", which can be done by making both parts equal, since they should have the same length.

`\begin{gathered} AB=BC \\ 15x=8x+28 \\ 15x-8x=28 \\ 7x=28 \\ x=(28)/(7) \\ x=4 \end{gathered}`

We can now use this value of "x" to determine the length of AC.

`\begin{gathered} AC=8x+28+15x \\ AC=23x+28 \end{gathered}`

Applying the value of x equal to 4, gives us:

`\begin{gathered} AC=23\cdot4+28 \\ AC=92+28 \\ AC=120 \end{gathered}`

The length of the segment AC is 120