Question

u is the midpoint of $overline{tv}$. if $tu = 9x$ and $tv = 12x + 8$, what is $tu$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since \(U\) is the mid - point of \(\overline{TV}\), then \(TV = 2TU\). Given \(TU = 9x\) and \(TV=12x + 8\), we have the equation \(12x + 8=2\times(9x)\).

Step2: Solve the equation for \(x\)

\[

$$\begin{align*} 12x + 8&=18x\\ 8&=18x-12x\\ 8&=6x\\ x&=\frac{8}{6}=\frac{4}{3} \end{align*}$$

\]

Step3: Find the value of \(TU\)

Substitute \(x = \frac{4}{3}\) into the expression for \(TU\). Since \(TU = 9x\), then \(TU=9\times\frac{4}{3}=12\).

Answer:

12