Question

g is the midpoint of $overline{fh}$. if $fg = 7x$ and $gh = 9x - 7$, 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 \(7x=9x - 7\).

Step2: Solve for \(x\)

Subtract \(7x\) from both sides: \(0 = 9x-7x - 7\), which simplifies to \(0 = 2x-7\). Then add 7 to both sides: \(2x=7\), and \(x=\frac{7}{2}\).

Step3: Find \(GH\)

Substitute \(x = \frac{7}{2}\) into the expression for \(GH\). \(GH=9x - 7\), so \(GH=9\times\frac{7}{2}-7=\frac{63}{2}-7=\frac{63}{2}-\frac{14}{2}=\frac{63 - 14}{2}=\frac{49}{2}=24\frac{1}{2}\).

Answer:

\(24\frac{1}{2}\)