Question

u is the midpoint of (overline{tv}). if (tu = 9x) and (uv=x + 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 midpoint of $\overline{TV}$, then $TU = UV$. So, $9x=x + 8$.

Step2: Solve for x

Subtract x from both sides: $9x−x=x + 8−x$. This gives $8x=8$. Then divide both sides by 8: $x = 1$.

Step3: Find TU

Substitute $x = 1$ into the expression for TU. Since $TU = 9x$, then $TU=9\times1=9$.

Answer:

9