Question

v is the midpoint of \\(\overline{uw}\\). if \\(uv = x + 4\\) and \\(vw = 3x\\), what is \\(vw\\)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use midpoint property

Since \( V \) is the midpoint of \( \overline{UW} \), \( UV = VW \). So we set up the equation \( x + 4 = 3x \).

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( 4 = 3x - x \), which simplifies to \( 4 = 2x \). Then divide both sides by 2: \( x=\frac{4}{2}=2 \).

Step3: Find \( VW \)

We know \( VW = 3x \), substitute \( x = 2 \) into it: \( VW = 3\times2 = 6 \).

Answer:

\( 6 \)