Question

use the given diagram. eh is the perpendicular bisector of df. find the measure of fg.
a 4
b 5
c 38
d 44

Explanation:

Step1: Use the property of perpendicular bisector

Since \(EH\) is the perpendicular bisector of \(DF\), \(EF = ED\) and \(GF=GD\).
We have \(7x + 9=9x - 1\).
Solve for \(x\):
\(9 + 1=9x - 7x\)
\(10 = 2x\)
\(x = 5\)

Step2: Solve for \(y\)

Also, \(7y+8 = 10y - 4\)
\(8 + 4=10y - 7y\)
\(12 = 3y\)
\(y = 4\)

Step3: Calculate \(FG\)

Substitute \(y = 4\) into \(7y+8\)
\(FG=7\times4 + 8\)
\(FG = 28+8\)
\(FG=36\)

Answer:

C. 36