Question

1. given: $overline{wz}perpoverline{vy}$, $overline{wz}$ bisects $overline{vy}$, $vz = 2x + 2$, and $zy = 3x - 4$. what is $vy$? 18 28 14 6

Explanation:

Step1: Use bisection property

Since $\overline{WZ}$ bisects $\overline{VY}$, we have $VZ = ZY$. So, $2x + 2=3x - 4$.

Step2: Solve for x

Subtract $2x$ from both sides: $2=x - 4$. Then add 4 to both sides, getting $x = 6$.

Step3: Find length of $VZ$ or $ZY$

Substitute $x = 6$ into the expression for $VZ$ (we could also use $ZY$). $VZ=2x + 2=2\times6+2=14$.

Step4: Calculate $VY$

Since $VY=VZ + ZY$ and $VZ = ZY$, $VY = 2VZ$. So, $VY=2\times14 = 28$.

Answer:

28