Question

f is the midpoint of $overline{eg}$. if $ef = 3x$ and $fg = x + 2$, what is $fg$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since F is the mid - point of $\overline{EG}$, then $EF = FG$. So we set up the equation $3x=x + 2$.

Step2: Solve the equation for x

Subtract x from both sides: $3x−x=x + 2−x$, which simplifies to $2x=2$. Then divide both sides by 2: $\frac{2x}{2}=\frac{2}{2}$, so $x = 1$.

Step3: Find the value of FG

Substitute $x = 1$ into the expression for FG. Since $FG=x + 2$, then $FG=1 + 2=3$.

Answer:

3