Question

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

Explanation:

Step1: Use property of perpendicular bisector

Since $FK$ is a perpendicular bisector of $GJ$, points on the perpendicular bisector are equidistant from the endpoints of the segment it bisects. So $GF = JF$.

Step2: Set up the equation

We have the equation $6 + x=3x - 5$.

Step3: Solve for x

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

Answer:

$x = 5.5$