Question

Point O is the centroid of triangle ABC. If FO = 2x -8 and FB = 3x + 3, find x

Answer 1

The centroid of a triangle is the geometric center of the triangle. It is the intersection point of the 3 medians in a triangle.

The centroid divides each median in a ratio of 2:1.

The median FB is divided into FO and OB in the ratio 1:2.

We can write >>>

`(FO)/(FB)=(1)/(3)`

Substituting the information we know, we can find "x". The steps are shown below >>>

`\begin{gathered} (FO)/(FB)=(1)/(3) \\ (2x-8)/(3x+3)=(1)/(3) \\ 3(2x-8)=1(3x+3) \\ 6x-24=3x+3 \\ 6x-3x=3+24 \\ 3x=27 \\ x=(27)/(3) \\ x=9 \end{gathered}`Answer
`x=9`