Question

1. if g is the mid - point of fh, fg = 14x + 25 and gh = 73 - 2x, find fh.

Explanation:

Step1: Use mid - point property

Since G is the mid - point of FH, then FG = GH. So, we set up the equation $14x + 25=73 - 2x$.

Step2: Solve the equation for x

Add $2x$ to both sides: $14x+2x + 25=73-2x + 2x$, which simplifies to $16x+25 = 73$. Then subtract 25 from both sides: $16x+25 - 25=73 - 25$, getting $16x=48$. Divide both sides by 16: $x=\frac{48}{16}=3$.

Step3: Find the length of FG or GH

Substitute $x = 3$ into the expression for FG. FG=$14\times3+25=42 + 25=67$. Since FH=FG + GH and FG = GH, then FH = 2FG.

Step4: Calculate FH

FH = 2×67 = 134.

Answer:

134