Question

g is the midpoint of $overline{fh}$. if $fg = 8x$ and $gh = x + 7$, what is $gh?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since G is the mid - point of $\overline{FH}$, then $FG = GH$. So we set up the equation $8x=x + 7$.

Step2: Solve the equation for x

Subtract x from both sides: $8x−x=x + 7−x$, which simplifies to $7x=7$. Then divide both sides by 7: $x = 1$.

Step3: Find the value of GH

Substitute $x = 1$ into the expression for $GH$. Since $GH=x + 7$, then $GH=1+7=8$.

Answer:

8