Question

u is the midpoint of $overline{tv}$. if $tu = 5x$ 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 mid - point of $\overline{TV}$, then $TU = UV$. So we set up the equation $5x=x + 8$.

Step2: Solve the equation for x

Subtract x from both sides: $5x−x=x + 8−x$, which simplifies to $4x=8$. Then divide both sides by 4: $x=\frac{8}{4}=2$.

Step3: Find the value of TU

Substitute $x = 2$ into the expression for TU. Since $TU = 5x$, then $TU=5\times2 = 10$.

Answer:

10