Question

u is the mid - point of (overline{tv}). if (tu = 2x + 8) and (uv = 4x - 8), what is (uv)? 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 $2x + 8=4x - 8$.

Step2: Solve for x

Subtract $2x$ from both sides: $8 = 4x-2x - 8$, which simplifies to $8 = 2x - 8$. Then add 8 to both sides: $8 + 8=2x$, so $16 = 2x$. Divide both sides by 2, we get $x = 8$.

Step3: Find the value of UV

Substitute $x = 8$ into the expression for $UV$. Since $UV=4x - 8$, then $UV=4\times8 - 8$. First, calculate $4\times8=32$, then $32-8 = 24$.

Answer:

24