Question

w is the midpoint of \\( \overline{vx} \\) and y is the midpoint of \\( \overline{ux} \\). if \\( uv = 18p \\) and \\( wy = 3p + 30 \\), what is wy?

Explanation:

Step1: Use the mid - segment theorem

Since \(W\) is the midpoint of \(\overline{VX}\) and \(Y\) is the midpoint of \(\overline{UX}\), by the mid - segment theorem in a triangle (\(WY=\frac{1}{2}UV\)).

Step2: Set up the equation

Given \(UV = 18p\) and \(WY=3p + 30\), and \(WY=\frac{1}{2}UV\), we substitute \(UV\) into the equation: \(3p + 30=\frac{1}{2}(18p)\).

Step3: Solve the equation for \(p\)

Simplify the right - hand side: \(3p + 30 = 9p\).
Subtract \(3p\) from both sides: \(30=9p - 3p\), so \(30 = 6p\).
Divide both sides by \(6\): \(p=\frac{30}{6}=5\).

Step4: Find the value of \(WY\)

Substitute \(p = 5\) into the expression for \(WY\): \(WY=3p+30\).
\(WY=3\times5 + 30\).
\(WY = 15+30\).

Answer:

\(WY = 45\)