Question

1. if g is the mid - point of $overline{eh}$, find fg. 11x - 7 3x + 9 f g h

Explanation:

Step1: Set up equation using mid - point property

Since \(G\) is the mid - point of \(\overline{FH}\), then \(FG = GH\). So, \(11x−7=3x + 9\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(11x-3x - 7=3x-3x + 9\), which simplifies to \(8x-7 = 9\). Then add 7 to both sides: \(8x-7 + 7=9 + 7\), getting \(8x=16\). Divide both sides by 8: \(x=\frac{16}{8}=2\).

Step3: Find \(FG\)

Substitute \(x = 2\) into the expression for \(FG\). \(FG=11x−7\), so \(FG=11\times2−7=22 - 7=15\).

Answer:

15