Question

in quadrilateral fgkj, (overline{fk}) is a perpendicular bisector of (overline{gj}). the length of segment (overline{gf}) is (6 + x) units, and the length of segment (overline{jf}) is (3x - 5) units. what is the value of (x)? (1 point) the value of (x) is

Explanation:

Step1: Use the property of perpendicular bisector

Since \(FK\) is a perpendicular bisector of \(GJ\), by the property of perpendicular bisector (any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment), we have \(GF = JF\).

Step2: Set up the equation

Given \(GF=6 + x\) and \(JF = 3x-5\), then the equation is \(6 + x=3x - 5\).

Step3: Solve the equation

Subtract \(x\) from both sides: \(6=3x - 5-x\), which simplifies to \(6 = 2x-5\).
Add \(5\) to both sides: \(6 + 5=2x\), so \(11 = 2x\).
Divide both sides by \(2\): \(x=\frac{11}{2}=5.5\).

Answer:

\(5.5\)