Question

u is the midpoint of \overline{tv}. if tu = 5x and uv = x + 8, what is uv?
simplify your answer and write it as a proper fraction, mixed number, or in

Explanation:

Step1: Use the midpoint property

Since \(U\) is the midpoint of \(\overline{TV}\), \(TU = UV\). So, \(5x=x + 8\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(5x-x=x + 8-x\), which gives \(4x=8\). Then divide both sides by \(4\): \(x=\frac{8}{4}=2\).

Step3: Find the value of \(UV\)

Substitute \(x = 2\) into \(UV=x + 8\). So, \(UV=2+8=10\).

Answer:

\(10\)