Question

what is the length of $overline{yz}$ when $y$ is the mid - point of $overline{xz}$?
a) 2
b) 10
c) 16
d) 20

Explanation:

Step1: Set up equation using mid - point property

Since \(Y\) is the mid - point of \(XZ\), then \(XY = YZ\). So, \(12 - x=3x + 4\).

Step2: Solve the equation for \(x\)

Add \(x\) to both sides: \(12=3x + 4+x\), which simplifies to \(12 = 4x+4\). Then subtract 4 from both sides: \(12−4 = 4x\), so \(8 = 4x\). Divide both sides by 4, we get \(x = 2\).

Step3: Find the length of \(YZ\)

Substitute \(x = 2\) into the expression for \(YZ\) which is \(3x + 4\). So \(YZ=3\times2 + 4=6 + 4=10\).

Answer:

B. 10