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=14x + 25=14×3 + 25=42 + 25=67. Since GH also equals 67 (because FG = GH).

Step4: Calculate FH

FH=FG + GH. Since FG = GH = 67, then FH=67+67 = 134.

Answer:

134