Question

x is the mid - point of $overline{wy}$. $wx = 8z+24$ and $wy = 96$. find $z$, $wx$, and $xy$

Explanation:

Step1: Use mid - point property

Since \(X\) is the mid - point of \(\overline{WY}\), then \(WX = XY\) and \(WY=WX + XY = 2WX\).

Step2: Set up equation for \(z\)

We know \(WY = 96\) and \(WX=8z + 24\), and \(WY = 2WX\). So \(96=2(8z + 24)\).
First, divide both sides of the equation by 2: \(\frac{96}{2}=8z + 24\), which simplifies to \(48=8z + 24\).
Then subtract 24 from both sides: \(48−24 = 8z\), so \(24 = 8z\).
Finally, divide both sides by 8: \(z=\frac{24}{8}=3\).

Step3: Find \(WX\)

Substitute \(z = 3\) into the expression for \(WX\): \(WX=8z + 24=8\times3+24=24 + 24=48\).

Step4: Find \(XY\)

Since \(XY = WX\), then \(XY = 48\).

Answer:

\(z = 3\)
\(WX = 48\)
\(XY = 48\)