Question

1. use the given diagram. ( eh ) is the perpendicular bisector of ( df ). find the value of ( y ).

a. 4
b. 5
c. 36
d. 44

Explanation:

Step1: Use the property of perpendicular bisector

Since \(EH\) is the perpendicular bisector of \(DF\), then \(EF = ED\) and \(FG=GD\).
For \(FG = GD\), we have \(7y + 8=10y-4\).

Step2: Solve the equation for \(y\)

Subtract \(7y\) from both sides: \(8 = 10y-7y - 4\), which simplifies to \(8=3y - 4\).
Add \(4\) to both sides: \(8 + 4=3y\), so \(12 = 3y\).
Divide both sides by \(3\): \(y=\frac{12}{3}=4\).

Answer:

A. 4